Mary Katherine Babb Randolph, 75, a volunteer in local Washington affairs for many years, a former social worker in her native West Virginia and the wife of Sen. Jennings Randolph (D-W.Va.), died of cancer Tuesday at her home in Washington.

From 1939 to 1946, when her husband, then a member of the House of Representatives, was chairman of the House District Committee, the Randolphs were considered the unofficial Mayor and First Lady of Washington. In those days, true power in local city affairs resided in the House committee and in the three District commissioners who were appointed by the president.

The Randolphs were married for 48 years and lived in Washington all of that time. In 1958, Rep. Randoph, who had first come to Congress as a supporter of President Franklin D. Roosevelt's New Deal, was elected to the Senate.

Apart from her interest in local Washington affairs, Mrs. Randolph was a close associate of Eleanor Roosevelt and of seven subsequent First Ladies, from Bess Truman to Rosalynn Carter. She was active in the Senate Wives Club and was a volunteer with civic and service groups, including the Heart Association, the Boys' Club, the Florence Crittenton Home and St. Patrick's Episcopal Church.

The daughter of a former mayor of Keyser, W.Va., Mrs. Randolph was born there on May 8, 1905. She graduated from Potomac State College and Beaver College in Jenkintown, Pa. Before her marriage to Sen. Randolph, she was a social worker for the West Virginia Board of Children's Guardians, now part of the Department of Public Welfare. She was in charge of child placement in 13 West Virginia counties. She also was a textile designer for a Keyser woolen mill. In 1979, Mrs. Randolph was awarded an honorary Doctor of Public Service degree from Salem College in West Virginia.

Besides her husband, survivors include two sons, Jay, of St. Louis, and Frank, of Washington, and three grandchildren.