No. The Federal Reserve does influence the rate you earn, however. The “Fed” controls something called the federal funds rate, which is the rate at which financial institutions lend money to one another overnight. That rate influences other short-term interest rates, including those for savings accounts.
So when the Fed raises the federal funds rate, savings account yields might get a bump — although the increase probably won’t be immediate or in lockstep. (And in fact, banks don’t have to raise your interest rates at all.