America Votes Act of 2021 This bill permits the use of sworn written statements to meet identification requirements for voting in federal elections. Specifically, an individual who is required to present identification as a condition of voting in a federal election may meet this requirement by presenting a sworn written statement attesting to the individual's identification and that he or she is registered to vote in the election. An individual who wants to vote by mail may submit such a statement with the ballot. States with an identification requirement must make copies of a preprinted version of the statement available for individuals to complete. Additionally, states must provide these individuals with a regular ballot instead of a provisional ballot. The bill does not apply to first-time voters registering by mail.