Question: Do Members of Congress pay Social Security taxes?
From the 2012 Congressional Research Service report Retirement Benefits for Members of Congress:
Members of Congress began to pay into Social Security in 1983, as part of a government-wide pension overhaul.
The 1983 amendments to the Social Security Act (P.L. 98-21) required all Members of Congress to participate in Social Security as of January 1, 1984, regardless of when they first entered Congress. The laws governing payment of Social Security taxes and eligibility for Social Security benefits apply to Members of Congress in the same way they apply to any other covered worker. Prior to 1984, neither federal civil service workers nor Members of Congress paid taxes to Social Security, nor were they eligible for Social Security benefits.
You can read the full Congressional Research Service report on Retirement Benefits for Members of Congress here.