They may participate in Social Security, however, their pension is not based on Social Security rates.
The law required all members of Congress to participate in Social Security as of January 1, 1984, regardless of when they first entered Congress. Because the CSRS was not designed to coordinate with Social Security, Congress directed the development of a new retirement plan for federal employees, called the Federal Employees Retirement System (FERS), which does coordinate a federal pension with Social Security.
Members of Congress are eligible for a pension at age 62 if they have completed at least five years of service. They are eligible for a pension at age 50 if they have completed 20 years of service, or at any age after completing 25 years of service. The amount of the pension depends on years of service and the average of the highest three years of salary. By law, the starting amount of a member’s retirement annuity may not exceed 80 percent of his or her final salary.
Not to exceed 80% of their salary? I would like to retire with a pension that is 80% of my salary... most people would.