Rostker was born in The Bronx in 1944 and graduated from Taft High School in June 1960 at the age of sixteen.

[9][10] In 1968, he reported for active duty in the Army and joined the Manpower Requirements Directorate of the Office of the Assistant Secretary of Defense for Systems Analysis as an economist.

He is the named defendant in the U.S. Supreme Court case of Rostker v. Goldberg, 453 U.S. 57 (1981), which upheld the constitutionality of requiring only men to register for selective service.

In 1983, he joined software development company SRA International as Director of the Systems Management Division.

President Clinton nominated Rostker as Under Secretary of the Army and he was sworn in on October 26, 1998, while retaining his responsibilities for Gulf War Illness issues.

After a nomination from President Clinton and confirmation by the United States Senate, Rostker was sworn in as the Under Secretary of Defense for Personnel and Readiness on May 23, 2000.

Rostker was replaced by David S. C. Chu, who was sworn in as Under Secretary of Defense for Personnel and Readiness on June 1, 2001.