If FICA was wrongly withheld from my paycheck as an exempt student, how do I get it refunded?

Start with your employer, since they can issue a corrected W-2 and refund the Social Security and Medicare tax more easily than the IRS can. If the employer refuses or can't, file Form 843 (Claim for Refund) plus Form 8316 stating the employer wouldn't refund it, and attach your W-2, visa, I-94, and proof of student status. You have generally three years from the filing date or two years from payment, whichever is later, to claim it. Keep copies of everything you send. This process only applies while you qualified as an exempt nonresident student. The IRS describes the refund path in Publication 519 at irs.gov.