If she is on an F1 student visa for less than 5 years or part years, she is exempt from paying FICA. If she is in the US on an F1 visa for more than 5 years or part years she is liable for FICA taxes and will need to work with her employer to correct this situation.
If she is in the US for less than 5 years or part years and you both choose to file married filing jointly, she is still exempt from FICA. The election to file married filing jointly does not affect her FICA exemption.
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