Parker was born Bronx, New York City. He was not formally trained as a classical player, though he did study with Jimmy Garrison, Richard Davis, and Wilbur Ware and learned the tradition. Parker is one of few jazz bassists who regularly plays arco. He also plays several other instruments from around the world, including the West African kora.
While Parker has been active since the early 1970s; he has had a higher public profile since the early 1990s. He is a prominent and influential musician in the New York City experimental jazz scene, and has regularly appeared at music festivals around the world, including the Guelph Jazz Festival, in southern Ontario.
Parker first came to public attention with pianist Cecil Taylor. He has long been a member of saxophonist David S. Ware's quartet and in Peter Brötzmann' s groups.
He is a member of the cooperative Other Dimensions In Music. Together with his wife, dancer Patricia Nicholson, he organizes the annual Vision Festival in New York City.
Parker has recorded and performed with many musicians, including Lewis "Flip" Barnes, Matthew Shipp, Hamid Drake, Frank Lowe, Daniel Carter,Louie Belogenis, Federico Ughi, Bill Dixon, Charles Gayle, Roscoe Mitchell, Butch Morris, Billy Bang, Fred Anderson, Kidd Jordan, Rob Brown, Joe Morris, Rashied Ali, Paul Murphy, Sunny Murray, Cooper-Moore, Perry Robinson, Barre Phillips, Henry Grimes, Peter Kowald, Spring Heel Jack, El-Producto, DJ Spooky, Susie Ibarra, Joel Futterman, Julia Kent, John Zorn, Mat Maneri, Nels Cline, Muhammad Ali, Thollem McDonas and Alan Juice Glover.