Rural Housing Accessibility Act This bill requires a public housing agency (PHA) that uses less than 95% of its budget authority in a given year to accept a housing choice voucher from a family that received the voucher from an agency in a different jurisdiction. The PHA that accepts the voucher (1) must make assistance payments to the family under an annual contributions contract, and (2) may not bill the initial PHA for the assistance payments for more than 12 months.