NOTE: This answer has been heavily rewritten. As requested it now discusses the opinions of Bible scholars on the subject.
The interpretation of the law in the infographic is not based on known historical facts. It is based on unfavorable and unproven assumptions about the culture to which it belonged, prejudices if you will. For this reason it is considered a slur against Judaism.
Few if any Jewish and Christian scholars believe that the girl was legally obliged to marry the man. What they do believe is that in that culture it was generally her best option for a normal life.
There is debate among scholars about what kind of sexual encounter is described in this law (more on this later), but Jewish and Christian commentators invariably see this law as protecting women’s rights. It is understood to create a right which an unmarried woman could enforce against a man who had sexually used and then abandoned her. For example, Matthew Henry (1662--1714) writes:
"If a damsel not betrothed were thus abused by violence, he that
abused her should be fined, the father should have the fine, and, if
he and the damsel did consent, he should be bound to marry her, and
never to divorce her, how much soever she was below him, and how
unpleasing soever she might afterwards be to him, as Tamar was to
Amnon after he had forced her, v. 28, v. 29. This was to deter men
from such vicious practices, which it is a shame that we are
necessitated to read and write of."
--Mathew Henry's Commentary of the Whole Bible--Old Testament, Deuteronomy 22:29
While the assertion that the girl was legally obliged to marry the man cannot be absolutely disproved (since the Bible records no cases where this law was invoked), it is widely seen as absurd, contrary to the intent of the law, and at odds with a similar law.
Scholars compare this law to the one at Exodus 22:16--17 which says that a man who has seduced a virgin girl must marry her. That law adds that "if her father absolutely refuses to give her" the offender has to pay the bride price anyway. This law is not granting the father any right he did not have before. It is simply acknowledging that in a society where marriages are arranged his permission is needed. Not mentioning this right again at Deuteronomy 22:29 does not necessary revoke it.
Commentary in the Mishneh Torah (12th century C.E.) supports such an interpretation:
When, however, a woman who is raped or her father do not desire that
she marry the rapist, they have that prerogative. [In such an
instance,] he must pay the fine and depart. If she and her father
desire [that the marriage take place], but he does not desire, we
force him to marry her, aside from paying the fine, as [Deuteronomy
22:29] states: "He must take [the maiden] as his wife"; this is a
positive commandment.
--Halacha 3
Matthew Poole (1624--1679) believed that the law at Deuteronomy 22:28,29 describes an offense more serious than seduction at Exodus 22:16--17 and therefor provides enhanced remedies:
Fifty shekels of silver, besides the dowry, as Philo the learned Jew
notes, which is here omitted, because that was common and customary,
and because it might easily be gathered out of Exodus 22:16, it being
sufficient here to mention what was peculiar to this case.
She shall be his wife, to wit, if her father consent to it, which is
to be supposed out of Exodus 22:16, it being not likely that the
father should lose his paternal right of disposing his child when she
was in some sort forced, rather than when she was enticed.
He may not put her away all his days, which others were suffered to
do, Deu 24:1, and he who enticed the maid (Exodus 22:16) was not
prohibited to do.
--Matthew Poole's English Annotations on the Holy Bible, Deuteronomy 22:29
From the above we see that Poole thinks it ridiculous to suppose that the father has no right to refuse just because that right is not specifically mentioned. If he can refuse a man who persuaded his daughter with words, surely he can refuse a man who used some degree of force.
Joseph Benson (1749--1821) similarly saw the man's obligation to marry as contingent on the permission of the woman's father:
"She shall be his wife — He was not at liberty to refuse her, if her
father consented to his marrying her, and he was deprived of the
privilege of ever divorcing her."
--Joseph Benson's Commentary of the Old and New Testaments, Deuteronomy 22:29
The description and illustration in the infographic are the product of a lurid imagination. A plainer description of Jewish law would be: “If a man rapes a married woman, he dies. If he rapes an unmarried woman she can make him marry her.”
But why would she want to? Probably because the 'rapist' is someone she knows and would have considered marrying.
Rapes Described in the Bible
Though the Bible does not describe any case where this law was enforced, it does describe two rapes of single women. These shed light on the cultural background of the law.
One is the rape of Dina described in Genesis chapter 34. While she was visiting young women in a nearby city a man named Shechem “took her and lay down with her and violated her”. Shechem persuaded her to marry him, sent his father to her father to arrange the marriage, and did marry her. But two of her brothers did not consider this an adequate remedy, so they went and murdered him and all his clan.
The second is the rape of Tamar described in 2 Samuel chapter 13. After she was raped by her half brother Amnon, she refused to leave the house, apparently on the basis that he now had to marry her. Her full blood brother Absalom hushed it up until he could murder Amnon in revenge.
Dina and her father (who knew about the rape) clearly believed that marriage with Shechem was now in her best interests. Tamar seems to have demanded marriage. They probably preferred an egotistical husband who did not know what "no" means to a lifetime of shameful singleness. There were few if any roles for single women, but it was not unheard of for married women to do all sorts of interesting things including managing family businesses (see Proverbs chapter 31).
So if a woman “had to marry her rapist” it was only in the sense that this was the less bad of two bad options. The law could not make her whole, but it could offer her this option.
Nature of the Sexual Encounter
I should mention that it is not certain that the offense described at Deuteronomy 22:28,29 is rape. A few modern translations such as the NIV use the word "rape", but most translations give a more literal reading. For example, where the NIV has "rapes" the KJV has "and lay hold on her, and lie with her".
John Gill (English theologian, 1697--1771) in his Exposition of the Whole Bible comments on Deuteronomy 22:28:
"and lay hold on her, and lie with her, she yielding to it, and so is
not expressive of a rape, as Deuteronomy 22:25 where a different word
from this is there used; which signifies taking strong hold of her,
and ravishing her by force; yet this, though owing to his first
violent seizure of her, and so different from what was obtained by
enticing words, professions of love, and promises of marriage, and the
like, as in Exodus 22:16 but not without her consent"
--John Gill's Exposition of the Whole Bible, Deuteronomy 22:28
Gill is comparing this law to the one that comes just before it in the text. In the previous law a woman who was "forced" into the sexual act is described as an innocent crime victim. In this case though Gill believes that “lay hold on her” means that the man grabbed her forcefully (which is what “violent” meant in Gill's day) and they had sex.
Bible commentator Dr. Greg L. Bahnsen (1948--1995) notes that the original language word translated "lay hold" does not by itself indicate a violent act:
The Hebrew word tapas (“lay hold of her,” emphasized above) simply
means to take hold of something, grasp it in hand, and (by
application) to capture or seize something. It is the verb used for
“handling” the harp and flute (Gen. 4:21), the sword (Ezek. 21:11;
30:21), the sickle (Jer. 50:16), the shield (Jer. 46:9), the oars
(Ezek. 27:29), and the bow (Amos 2:15). It is likewise used for
“taking” God’s name (Prov. 30:9) or “dealing” with the law of God
(Jer. 2:8). Joseph’s garment was “grasped” (Gen. 39:12; cf. I Kings
11:30), even as Moses “took” the two tablets of the law (Deut. 9:17).
People are “caught” (I Kings 20:18), even as cities are “captured”
(Deut. 20:19; Isa. 36:1). An adulterous wife may not have been
“caught” in the act (Num. 5:13). In all of these instances it is clear
that, while force may come into the picture from further description,
the Hebrew verb “to handle, grasp, capture” does not in itself
indicate anything about the use of force.
--Greg L. Bahnsen, Pre-Marital Sexual Relations: What is the Moral Obligation When Repeated Incidents are Confessed?
Bible translations reflect the various ways in which this expression has been understood:
Geneva Bible (1599):
If a man find a maid that is not betrothed, and take her, and lie with her, and they be found,
King James Version: (1611):
If a man find a damsel that is a virgin, which is not betrothed, and lay hold on her, and lie with her, and they be found;
Douay-Rheims (1899):
If a man find a damsel that is a virgin, who is not espoused, and taking her, lie with her, and the matter come to judgment:
American Standard Version (1900):
If a man find a damsel that is a virgin, that is not betrothed, and lay hold on her, and lie with her, and they be found;
Living Bible (1971):
If a man rapes a girl who is not engaged and is caught in the act,
Contemporary English Version (1995):
Suppose a woman isn’t engaged to be married, and a man talks her into sleeping with him. If they are caught,
Complete Jewish Bible (1998):
If a man comes upon a girl who is a virgin but who is not engaged, and he grabs her and has sexual relations with her, and they are caught in the act,
New English Translation (2005):
Suppose a man comes across a virgin who is not engaged and overpowers and rapes her and they are discovered.
Modern English Version (2014):
If a man finds a girl who is a virgin who is not engaged and seizes her and lies with her and they are discovered,
Some translators have compared this passage to other similar passages and concluded that non-consensual intercourse is meant, but the text does not really make that clear. That may be deliberate. If the sexual act itself is sufficient to trigger the law's remedies, then there is no need for the judges to determine whether the act was consensual before applying this particular law.
(Copied from http://www.theliberaloc.com/2012/05/14/traditional-marriage-according-to-the-bible/)
