F.I.C.A. stands for the Federal Insurance Contributions Act which is a taxation on income earned where the funds are used for federal programs that provide benefits for U.S. citizens and permanent residents when they retire, are disabled, or are the children of deceased workers. Funds withheld for F.I.C.A. are reflected on paycheck stubs and also in boxes 4 and 6 of your W-2.
Internationals and F.I.C.A.
F-1 and J-1 student visa holders are typically exempt from paying F.I.C.A. taxes for their first 5 years in the United States and these taxes should not be deducted from paychecks. J-1 scholars and researchers are typically only exempt for 2 years. The mechanism for the exemptions are found under Internal Revenue Code 3121 (b)(19) and is available to persons in F-1, J-1, M-1 and Q immigration status.
It is a blanket exemption with the only qualification being that the person be a nonresident for tax purposes and that the work is authorized (CPT, OPT, AT). IRS Publication 519 is a good resource, specifically pages 44 and 45. More information is available here.
Obtaining Reimbursements of F.I.C.A. Witholdings
If your employer has mistakenly withheld F.I.C.A. taxes, you must work with them directly to request a reimbursement. If they will not assist you, you can file Internal Revenue Service (IRS) forms 843 or 8316 to request reimbursement. Please note that J-2s with work authorization are not exempt from FICA taxes.
Assistance with filling out request for FICA reimbursement - University of Texas - Austin