Are NRAs automatically exempt from FICA (Medicare) tax?

No. Your visa type determines when you are exempt and when you are taxed for Medicare.

VISA types

FICA

 

F-1  based on student enrollment

Exempt for the first 5 years from the date of entry; may be exempt

J-1 Student enrollment

Exempt for the first 5 years from the date of entry; may be exempt based on student

J-1 scholars, Research

Exempt for either the first 2 calendar years in the US, or 2 out of the first 6 calendar years in the US regardless of visa status.  

F-2, J-2, H-1B, O-1, TN

Must pay FICA (Medicare)