International Medical Graduates Assistance Act of 2022 This bill authorizes grants and makes other changes to facilitate the practice of medicine by international medical graduates who are lawfully present in the United States and graduated from a medical school outside of the United States or Canada. Specifically, the Department of Health and Human Services may award grants for states and territories to establish programs that allow such international medical graduates to practice medicine under the supervision of a licensed physician while completing the first two steps of the U.S. Medical Licensing Examination, and provide assistance (e.g., costs to take the U.S. Medical Licensing Examination and career counseling) to such international medical graduates. The bill also exempts under certain circumstances such international medical graduates from the cap on full-time equivalent residents that is otherwise applicable for purposes of graduate medical education payments under Medicare.