Turner was born in Springfield, Missouri, the daughter of Patsy (née Magee) and Allen Richard Turner, a U.S. Foreign Service officer who grew up in China (where Turner's great-grandfather had been a Methodist Christian missionary). Her father, a diplomat, had been illegally imprisoned by the Japanese Empire for four years during the World War II. As a girl, Turner lived in Canada, Venezuela, and England, and she was living in Cuba at the time that Fidel Castro took over the government. When the United States soon after broke off diplomatic relations with Cuba, it forced the staff members of the American embassy in Havana to leave the country. Turner has two brothers and one sister. While attending high school in England, she was a gymnast, and she also took classes at the Central School of Speech and Drama.
In her early years, Turner was interested in performing. Her father did not encourage her: "My father was of missionary stock," she later explained, "so theater and acting were just one step up from being a streetwalker, you know? So when I was performing in school, he would drive my mom [there] and sit in the car. She'd come out at intermissions and tell him, 'She's doing very well.'"
In her early years, Turner was interested in performing. Her father did not encourage her: "My father was of missionary stock," she later explained, "so theater and acting were just one step up from being a streetwalker, you know? So when I was performing in school, he would drive my mom [there] and sit in the car. She'd come out at intermissions and tell him, 'She's doing very well.'"