He was promoted... To Captain.
Comics Steve was a private or a corporal, depending on the writer. Such a low rank was in place as part of his secret identity.
After he "died", or at some point after coming back, he was promoted to Captain.
or when the army though him to have died in the crash of the skull's plane he was given a posthumous promotion
Never really saw the point of having Steve have Cap as a secret identity inside the Army, sounds like he would go through a hell of a lot of trouble to keep it secret and constantly change missions from Steve Rogers's and Captain America.