Housing Access Improvement Act This bill increases from 20% to 50% the amount of funding for the Housing Choice Voucher program that a public housing agency (PHA) may use for project-based vouchers. (This program subsidizes rent for low-income recipients.) Under current law, a PHA must use at least 80% of its funding for tenant-based vouchers (which subsidize recipients' rental of any private apartment that meets program guidelines) and may use up to 20% of its funding for project-based vouchers (which attach to a specific rental unit that the landlord commits to make available for voucher recipients for a contracted term).