PFAS Registry Act of 2021 This bill directs the Department of Veterans Affairs (VA) to establish a registry for current or past members of the Armed Forces who may have been exposed to per- and polyfluoroalkyl substances due to the environmental release of aqueous film-forming foam at a military installation or other Department of Defense (DOD) location. Additionally, the VA must consult with DOD and the Environmental Protection Agency to make recommendations for additional chemicals that should be included in the registry.