You can use Marriott points at a Ritz Carlton - http://marriott.com/rewards/usepoints/hotelpart.mi#54 - but you can't earn Marriott points at Ritz Carlton - http://marriott.com/rewards/earn/earnptshotel.mi - AFAIK, Ritz doesn't have an affinity program. You can use Amtrak points to stay at a Ritz too, FYI.

Marriott also owns the Ramada International brand too (not the domestic ones, only the International ones) & they are not part of Marriott Rewards. See the above sites for information.