If you only have an iPhone (without any RFID/NFC reader adapter), the answer is no. Current iPhones (we will see what features the iPhone 6 will bring us in that direction ...) do not have the necessary hardware to interact with MIFARE Classic chips (which -- in your case -- would be a 13.56 MHz iductive-coupling proximity reader with MIFARE Classic crypto support).
If your iPhone already has an NFC (or RFID) reader adapter, the answer depends on what specific adapter you use.
EDIT: As of today, this answer partially(!) applies to iPhone 6 (also see this question). The iPhone 6 has the necessary hardware to access such cards (i.e. an NFC controller chip from NXP), however there is no API that provides access to NFC reader/writer functionality. Moreover, there is doubts that the antenna boosting circuitry permits using the iPhone in reader/writer mode.