Yes, it's called SIPC and is (kind of) equivalent to the FDIC for banks. However it only covers up to $500k, only covers cash, stocks, bonds, CDs, and (I think) mutual funds. It does not cover options or future contracts.
Also it will only attempt to return the securities you 'lost' not their cash value. If you lose a lot of money due to not being able to sell your stocks for several days, that is not covered. So if you held 2000 stocks of GME, the SIPC will (eventually) give you back 2000 stocks of GME, not the cash value of those stocks when Robinhood went bankrupt.
Also it will only attempt to return the securities you 'lost' not their cash value. If you lose a lot of money due to not being able to sell your stocks for several days, that is not covered. So if you held 2000 stocks of GME, the SIPC will (eventually) give you back 2000 stocks of GME, not the cash value of those stocks when Robinhood went bankrupt.