Building Credit Access for Veterans Act of 2021 This bill requires the Department of Veterans Affairs (VA) to implement a pilot program to assess the feasibility and advisability of using alternative credit scoring information or models to improve the determination of creditworthiness of certain individuals and to increase the number of such individuals who are able to obtain VA housing and small business loans. Specifically, the program is for veterans or members of the Armed Forces who are eligible for VA housing or small business loans and have insufficient credit history. Under the program, the VA must assess the feasibility and advisability of establishing criteria for acceptable commercially available credit scoring models to be used by lenders for the purpose of guaranteeing or insuring a VA housing or small business loan. Participation is voluntary on an opt-in basis for lenders, borrowers, and individuals. The VA must conduct outreach to lenders and individuals to inform them of the pilot program.