Parker was born in Fort Jackson, South Carolina. Her mother, Caroline Louise (née Morell), was of part Swedish descent, and her father, John Morgan Parker, was a judge who served in the U.S. Army. Because of her father's career, Parker spent parts of her childhood in Tennessee and Texas, as well as in Thailand, Germany, and France. Parker majored in drama at the North Carolina School of the Arts.
Parker got her start in a bit part on the soap opera Ryan's Hope. In the late 1980s, Parker moved to New York, where she got a job measuring feet at ECCO. After a few minor roles, she made her Broadway debut in a 1990 production of Craig Lucas' Prelude to a Kiss, playing the lead role of Rita. She moved with the production when it transferred from its origin Off-Broadway. She won the Clarence Derwent Award for her performance and was nominated for a Tony Award (although she did not play the role when the film was made). Parker also briefly dated her co-star Timothy Hutton during this time.
Parker got her start in a bit part on the soap opera Ryan's Hope. In the late 1980s, Parker moved to New York, where she got a job measuring feet at ECCO. After a few minor roles, she made her Broadway debut in a 1990 production of Craig Lucas' Prelude to a Kiss, playing the lead role of Rita. She moved with the production when it transferred from its origin Off-Broadway. She won the Clarence Derwent Award for her performance and was nominated for a Tony Award (although she did not play the role when the film was made). Parker also briefly dated her co-star Timothy Hutton during this time.