Rent Relief Act of 2023 This bill allows a refundable income tax credit for individuals who pay rent for a principal residence that exceeds 30% of their adjusted gross income for the taxable year. The amount of the credit ranges from 25% to 100% of the excess rent, depending on the adjusted gross income of the taxpayer. The credit is not available for taxpayers with adjusted gross incomes that exceed $100,000. Rent that exceeds 100% of the small area fair market rent (including the utility allowance) for the residence may not be taken into account in determining the amount of the credit. The Department of the Treasury must establish a program for making advance payments of the credit on a monthly basis and provide for an outreach program to increase enrollment of taxpayers in the renter tax credit program.