Elizabeth Buxsel Gorham, 64, who was active in the Arlington League of Women Voters, died of cancer Thursday at Arlington Hospital after a brief illness.

Born in Cincinnati, she first came here in the 1930s to work for the Labor Department.

In 1953, she and her husband, James E. Gorham, now senior transportation economist with SRI international, moved to New Jersey and then to California.

In California, Mrs. Gorham decided to get the college degree she had missed in earlier years. Among the schools she attended was Pasadena City College, where she won a number of awards for academic excellence in literature, English and social sciences.

Mrs. Gorham received a bachelor's degree in history from California State University Women, serving as a branch area representative for international relations. She also was chairwoman of the trade and international relations study committee of the League of Women Voters of Arlington and participated in a recent study of Arlington County's tax base and budget. She was a volunteer worker for Common Cause.

In addition to her husband, she is survived by a son, Dr. R. Wilson Gorham, both of the home in Arlington; another son, Kenneth D., of Los Angeles; a daughter, Patricia Santanello, of Toms River, N.J.; a brother, William Buxsel, and a sister, Alice Glueck, both of Cincinnati, and three grandchildren.

The family suggests that expressions of sympathy may be in the form of contributions to the Linus Pauling Institute of Science and Medicine in Menlo Park, Calif.