Born in Charlotte, North Carolina, Parker attended Meredith College, graduated from the University of North Carolina at Chapel Hill with an Education degree and served with the Peace Corps in Turkey from 1964 to 1966 before returning to Chapel Hill to earn a J.D.

After working in private law practice for 15 years, Parker was named by Governor Jim Hunt to the North Carolina Court of Appeals in late 1984.

On January 19, 2006, Governor Mike Easley announced that he was appointing Parker Chief Justice of the Supreme Court, to replace the retiring I. Beverly Lake Jr. Parker took the oath of office on February 6, becoming the third female Chief Justice of North Carolina's highest court, after Susie Sharp and Rhoda Billings.

At the time of her appointment, former justice Bob Orr, a Republican and executive director of the N.C. Institute for Constitutional Law, was quoted in the Charlotte Observer calling Parker "probably one of the more conservative justices that has been on the court in a good long while.... She's going to be reluctant to go out on a limb.... My sense is that you would find very few cases that were close to the line where she favored criminal defendants."

[5] Governor Pat McCrory appointed Mark Martin, the court's senior Associate Justice, to replace her through the 2014 election.