Connect America Act of 2021 This bill requires the Federal Communications Commission to establish a funding program to expand broadband access for unserved areas, areas with low-tier or mid-tier service, and unserved anchor institutions (e.g., schools or libraries). The program shall consist of both national systems of competitive bidding and grants of specified amounts to states. An area with low-tier service is an area where at least 90% of the population has access to broadband service with speeds between 25-100 megabits per second (mbps). An area with mid-tier service is an area where at least 90% of the population has access to broadband service with speeds between 100 mbps and 1 gigabit per second. Priority must be given to projects that would expand access to broadband service in areas where at least 90% of the population has no access to broadband service or to service with speeds of at least 25 mbps.