Small Business Access to Capital Act of 2021 This bill reauthorizes for an additional eight years the State Small Business Credit Initiative. The initative assists participating states in providing collateral financial support to, and other innovative credit access and guarantee initiatives for, small businesses and manufacturers. The bill prescribes allocations of federal funds to participating states, and it authorizes the Department of the Treasury to award up to $5 billion in two tranches (portions), according to specified criteria, for participating states to (1) make federal contributions to an approved state program, or (2) use as collateral for a qualifying loan or swap funding facility.