Federal Bureau of Prisons Voting Assistance Act of 2021 This bill requires the Bureau of Prisons (BOP) to provide information about voting to inmates from jurisdictions that allow inmates to vote while in custody. Specifically, before a federal, state, or local election, the BOP must send inmates voting-related information, such as how to register to vote and how to request an absentee ballot. The BOP must send additional voting-related information to the reentry affairs coordinator at each federal correctional facility. The information must be provided in English and Spanish.