Rodriguez, 27, hit .213 with six home runs and 32 RBIs in 112 games with the Rays in 2012, while being used at third base, shortstop, second base and as a designated hitter.
Rodriguez was Tampa Bay's Opening Day shortstop, and he began the year in a platoon with Reid Brignac. Rodriguez was optioned to Triple-A Durham on Aug. 20, when Luke Scott was activated from the 15-day disabled list.
Rodriguez sustained a right hand fracture in an off-the-field injury on Aug. 26 after playing two games for Durham.
Rodriguez was acquired by the Rays in the 2009 trade that sent Scott Kazmir to the Angels.
Bill Chastain is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.