Ann Turner Thompson, 57, the press secretary of Mrs. Spiro T. Agnew when her husband was vice president of the United States, died of cancer July 12 at her home in Annapolis.

Mrs. Thompson, who was born in Memphis, Tenn., graduated from the University of Missouri in 1947 with a degree in journalism. She moved to the Annapolis area about 1950. From 1964 to 1968, she was a part-time Annapolis correspondent for The New York Times.

Her husband, Herbert L. Thompson, a former Associated Press correspondent, was Agnew's press secretary when he was governor of Maryland. When Agnew became vice president in 1969, Mr. Thompson joined his staff in Washington. Mrs. Thompson became Mrs. Agnew's press secretary and held that post until 1973, when Agnew resigned from office.

The Thompsons then moved to Tunisia, where Mr. Thompson was stationed with the State Department. In 1978, they moved to Hyderabad, India, where Mr. Thompson is head of the International Crops Research Institute for Semi-Arid Tropics, which is funded by the World Bank and the United Nations. Mrs. Thompson returned to Annapolis because of ill health.

She was president of the American Women's Club in Tunisia and a member of the Severn Town and Pan-Hellenic clubs and the Calvary United Methodist Church in Annapolis. For many years she was publicity chairman of the Anne Arundel County Fair.

In addition to her husband, of Annapolis, survivors include two daughters, Sally Leigh Stephens of Annapolis and Sheryl Scott Lawrence of Lake Lincolndale, N.Y.; her mother, Mildred L. Turner of Annapolis, and five grandchildren.