Prior to playing professional baseball, Rheinecker attended Belleville Area Community College and Southwest Missouri State.

On March 31, 2006, Oakland traded him (along with infielder Freddie Bynum) to the Texas Rangers for pitcher Juan Dominguez.

A southpaw starting pitcher, Rheinecker made his major league debut April 22, 2006, in a game against the Tampa Bay Devil Rays.

On his 27th birthday (May 29, 2006, which was also Memorial Day), Rheinecker made his second start for the Rangers, pitching 81⁄3 shutout innings and earning his first major league win.

Rheinecker was diagnosed with thoracic outlet syndrome (TOS) and underwent surgery to remove a rib to alleviate the symptoms.