No. You do not have to pay Social Security or Medicare tax because you are not working for a U.S. employer.
Revenue Ruling 92-106 says:
A foreign person is not an "American employer" as defined in sections 3121 (h) and 3306(j)(3) of the Code. Therefore, because the individual is performing services outside the United States, and· the individual's employer is not an "American employer", services performed by an employee are not included within the definition of "employment" for FICA and FUTA purposes. Therefore, remuneration paid the employee is not wages for FICA and FUTA purposes.
See page 259 of Internal Revenue Cumulative Bulletin 1992 [2]
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