Parker was born in Los Angeles, California, the only child of Actress Shirley MacLaine and businessman Steve Parker (1922–2001). At age two, Parker was sent to Japan to live with her father. During the summer and at holidays, Parker visited her mother, and they posed together on the cover of the February 9, 1959, issue of Life). Her maternal uncle is actor Warren Beatty.
Parker was married to investment banker Frank Murray from 1993 to 2011, and they lived for a time in Houston, Texas, while Murray was the President of Goodman Holdings. Parker and Murray have two children, a son, Frank Murray Jr. (born 1996), and a daughter, Arin Murray (born 1998).
Parker's work includes television appearances on Star Trek: The Next Generation, Equal Justice, and Alien Nation, and small film roles in Stick, About Last Night..., Peggy Sue Got Married and Bad Influence. Parker has also done small local theater. Parker starred in the 2009 Japanese film The Witch of the West Is Dead, which showed at the Palm Springs International Film Festival.
On February 7, 2013, the Penguin Group published Parker's autobiography, Lucky Me: My Life With – and Without – My Mom, Shirley MacLaine. MacLaine has called the book "virtually all fiction".
