Currently this option is not available in fabric framework.
https://dev.twitter.com/twitter-kit/android/compose
Note:
In the event that the Twitter app is not installed, TweetComposer will create an intent to interact with the Twitter.com in a browser. The browser ignores a specified image..
You can publish tweet using rest API
https://dev.twitter.com/rest/reference/post/statuses/update_with_media
POST /1.1/statuses/update_with_media.json HTTP/1.1
Host: api.twitter.com
User-Agent: Go http package
Content-Length: 15532
Authorization: OAuth oauth_consumer_key="...", oauth_nonce="...", oauth_signature="...", oauth_signature_method="HMAC-SHA1", oauth_timestamp="1347058301", oauth_token="...", oauth_version="1.0"
Content-Type: multipart/form-data;boundary=cce6735153bf14e47e999e68bb183e70a1fa7fc89722fc1efdf03a917340
Accept-Encoding: gzip
--cce6735153bf14e47e999e68bb183e70a1fa7fc89722fc1efdf03a917340
Content-Disposition: form-data; name="status" Hello 2012-09-07 15:51:41.375247 -0700 PDT!
--cce6735153bf14e47e999e68bb183e70a1fa7fc89722fc1efdf03a917340
Content-Type: application/octet-stream
Content-Disposition: form-data; name="media[]"; filename="media.png" ...
--cce6735153bf14e47e999e68bb183e70a1fa7fc89722fc1efdf03a917340--