Choice in Affordable Housing Act of 2022 This bill establishes programs and grants to incentivize landlord participation in the Housing Choice Voucher program (i.e., Section 8 tenant-based housing assistance). The bill authorizes the Department of Housing and Urban Development (HUD) to provide one-time incentive payments to landlords, security deposit payments, bonuses to public housing agencies that employ landlord liaisons, and amounts for other recruitment purposes. Additionally, the bill allows dwelling units to meet Housing Choice Voucher program inspection requirements by satisfactory inspection through participation in other housing programs. Landlords not yet participating in a low-income housing assistance program may request inspection by a public housing agency to determine whether the dwelling meets requirements prior to selection by a tenant. Finally, HUD must expand the use of an alternative method of calculating fair market rent for purposes of the Housing Choice Voucher program.