Rent Relief Act of 2022 This bill allows a refundable tax credit through 2024 for individuals who pay rent for a principal residence that exceeds 30% of their gross income for the taxable year. The amount of the credit ranges from 25% to 100% of the excess rent, depending on the gross income of the taxpayer. The credit is not available for taxpayers with gross income that exceeds $100,000 ($125,000 for a taxpayer whose principal residence is located in a high-cost area, as defined by the bill). Rent that exceeds 100% of the small area fair market rent (including the utility allowance) for the residence may not be taken into account for the purpose of determining the amount of the credit. For individuals who reside in government-subsidized housing, the bill allows a credit equal to 1/12th of the rent paid by the taxpayer (and not subsidized under the program) during the year with respect to the residence. The Department of the Treasury must establish a program for making advance payments of the credit on a monthly basis.