He was a descendent of William Bradford, a founder of Plymouth Colony, in Massachusetts, and of associate justice of the Supreme Court of the United States James Iredell.

[1] Parker received a Bachelor of Arts degree in 1907 from the University of North Carolina at Chapel Hill, where he was elected to membership in Phi Beta Kappa and was class president.

He was tasked with prosecution of former Wilson Administration officials for alleged frauds associated with World War I demobilization.

[3] Parker received a recess appointment from President Calvin Coolidge on October 3, 1925, to a seat on the United States Court of Appeals for the Fourth Circuit vacated by Judge Charles Albert Woods.

[3] On March 21, 1930, Parker was nominated by President Herbert Hoover as an Associate Justice of the United States Supreme Court[4] to fill the vacancy caused by the death of Edward Terry Sanford.

AFL president William Green[6] specifically faulted Parker for a 1926 Fourth Circuit Court decision which he authored regarding the United Mine Workers, involving antitrust law and yellow-dog contracts.

[2] The NAACP joined the opposition in response to remarks Parker had made while a candidate for governor in 1920 about the participation of African Americans in the political process: The participation of the Negro in politics is a source of evil and danger to both races and is not desired by the wise men in either race or by the Republican Party of North Carolina.

[4][5] From 1945 to 1946, Parker served as an alternate judge on the International Allied Military Tribunal at Nuremberg, Germany.