There have been a lot of players who served in the military, either before or during their career. Almost all of them, however, did so either during wartime or when we still had a draft.
Since the end of the Vietnam War, however, not many have. Mitch Harris, who pitched for the Cardinals last year, is a graduate of the Naval Academy and served. There may have been some other guys who served in the reserves, but not many. And in all cases, these guys did so before becoming established players, if indeed they ever did so.
Cardinals catcher Brayan Pena is an established player.