Affordable Housing Credit Improvement Act of 2021 This bill revises provisions of the low-income housing tax credit and renames it as the affordable housing credit . The bill increases the per capita dollar amount of the credit and its minimum ceiling amount beginning in 2021 and extends the inflation adjustment for such amounts. The bill modifies tenant income eligibility requirements and the average income formula for determining such income. It also revises rules for student occupancy of rental units and tenant voucher payments, and prohibits any refusal to rent to victims of domestic abuse. The bill further modifies the credit to increase state allocations of the credit; repeal the qualified census tract population cap; prohibit local approval and contribution requirements; increase the credit for certain projects designated to serve extremely low-income households; increase the credit for certain bond-financed projects designated by state agencies; eliminate the basis reduction for properties that receive certain energy-related tax benefits; and increase the population cap for difficult development areas (i.e., areas with high construction, land, and utility costs relative to area median gross income). The bill also includes Indian and rural areas as difficult development areas and modifies other requirements relating to casualty losses, acquisition credits, and foreclosures.