Rural Physician Workforce Production Act of 2021 This bill allows certain hospitals to receive additional payment under Medicare for full-time equivalent residents who receive training in rural areas. Specifically, hospitals, critical access hospitals, sole community hospitals, and rural emergency hospitals may elect to receive payment for time spent by a resident in a rural training location if the resident trains for at least eight weeks in the location and the hospital pays the salary and benefits of the resident during this time. Additionally, hospitals may receive payment for all time spent by residents in a residency program in which 50% of all training is in rural locations, regardless of where the training occurs or specialty. Payments are based on the difference between the total amount of eligible payments (as determined by the Centers for Medicare & Medicaid Services) and the amount of graduate medical education payments received (if applicable).