Parker graduated from Senn High School in Chicago. She went on to receive a B.A. from Northwestern University (1966). While in college she won an award from the student chapter of the American Institute of Chemists for her essay "Chemistry as a Profession" making her the first woman to receive this award. She earned her Ph.D. from Stanford University in 1970. Following her Ph.D. she was a postdoctoral research at Columbia University. From 1973 until 2001 Parker was in the chemistry department at Brown University. In 2001 she moved to Stony Brook University, and in 2017 she was named a distinguished professor at Stony Brook University.