The following classes of nonimmigrants and nonresident aliens are exempt from U.S. Social Security and Medicare taxes: A-visas. Employees of foreign governments are exempt on salaries paid to them in their official capacities as foreign government employees. read more
Short answer is for up to five years, F-1 visa students are exempt from FICA as long as they are a student employee, professor, teacher, researcher, au pair, or summer camp worker. The exemption does not apply to spouse or children. read more