Should I pay back FICA taxes if I'm a resident alien for tax purposes?

Question

I'm a resident alien for tax purposes (F-1 grad student), but my employer (my University) failed to withhold FICA taxes last year.

Should I be worried about this and how can I pay back taxes to FICA if so?

Answer 1

You are okay.  There is a SEPARATE law that states that full time students do not pay Fica/MC.  This separate law covers US Citizens, Resident Aliens and Non-Resident aliens.  

Answer 2

To clarify, what v b wrote applies only to work done for the educational institution where one is a student.  Full-time students who also work off-campus in the private sector (delivering pizza, for example) are not exempt.