She graduated from Sarah Lawrence College in Yonkers, New York, in 1945, as a chemistry major.
Her father specified in his will that a museum specializing in Western American art to be created after his death in 1955, to house his more than 700 art objects depicting the American West, primarily paintings and sculptures by Frederic Remington and Charles Russell. Stevenson hired architect Philip Johnson to design the building and opened the Amon Carter Museum of Western Art in January 1961, following her father"s wishes. She was the first president of the museum"s board of trustees and was president at her death in 2013.
Stevenson was also the first woman to be appointed to the board of directors of the National Gallery of Art in Washington, District of Columbia, and the first woman to become the chairman of that board.
Along with local art enthusiasts Owen Day and Sam Cantey III, Stephenson assembled An Art Exhibition for the President and Mistress John F. Kennedy which decorated the suite in the Hotel Texas in Fort Worth, Texas, occupied by United States President John F. Kennedy and Jacqueline Kennedy on the night before his assassination on November 22, 1963.
Ruth Carter Stevenson died at her home in Fort Worth, Texas, on January 6, 2013, at the age of 89.
Stevenson served as a Legislative Aide to two Essex County members of the New Jersey General Assembly, Beatrice Stiles from 1960 to 1961, and Frederic Remington from 1978 to 1982.
Married J. Lee Johnson III, June8, 1946 (divorced February 1978). Children: Sheila Broderick Johnson, J. Lee, Karen Carter Johnson Hixon, Catherine Johnson Tekstar, Mark Lehane;m. John R. Stevenson, May 21, 1983.