Cardozo was very active both in the medical community and as a volunteer in Washington, D.C. He was a member of the American Academy of Pediatrics, the Medical Society of the District of Columbia, the Advisory Committee of the District of Columbia Crippled Children's Society, the National Medical Association, the Alpha Phi Alpha Fraternity, and the Alpha Omega Alpha Honor Medical Society. Cardozo was elected the western vice president of the Alpha Phi Alpha Fraternity in 1930, while he was still a student at The Ohio State University. He also founded the Howard University branch of the Alpha Omega Alpha Honor Medical Society and was serving as its secretary and treasurer at the time of his death. Cardozo's volunteer activities included serving as a medical staffer at the Ionia R. Whipper Home for Unwed Mothers, as a council member on the D.C. Health and Welfare Council, and as an advisor on the Rock Creek East Neighborhood League.
