Yes Yellowstone National Park does allow RV's and Travel Trailers in the park.
In Yellowstone National Park they have campgrounds dedicated to parking RV's and Travel Trailers where you can pay a daily fee and have electricity and water.
If you want to camp in your RV or Travel Trailer somewhere else in the Yellowstone National Park then you can usually do so because I've seen a few campers and other RV's parked elsewhere away from the RV parks in Yellowstone.
You just won't have your electricity or running water but you can have your water tanks filled and use that and possibly use a generator during the day when dry camping in Yellowstone National Park.