Rural Connectivity Advancement Program Act of 2021 This bill sets aside 10% of the net proceeds from spectrum auctions to be deposited into a Rural Broadband Assessment and Deployment Fund, which shall be used for the buildout of broadband networks. The Federal Communications Commission (FCC) must use the fund to establish one or more programs to address (1) gaps in broadband internet access service coverage in high-cost rural areas, and (2) insufficient funding of other programs that could adversely affect the sustainability of broadband services or comparability of rates supported by such programs. Further, the FCC must establish transparency and accountability requirements for addressing such coverage gaps and funding shortfalls, and it must report annually on the distribution of amounts from the fund.