Rodriguez was designated for assignment by the Rays on Saturday and will head overseas to pitch in Japan, Marc Topkin of the Tampa Bay Times reports.
Rodriguez struck out five over 3.1 perfect innings during Friday's 2-1 loss against Atlanta.
The Rays selected Rodriguez from Triple-A Durham on Friday, Tricia Whitaker of Bally Sports Sun reports.
Rodriguez (elbow) was reinstated from Triple-A Durham's 7-day injured list Sunday and covered three innings while striking out two and allowing one run on three hits and one walk in his return to the rotation.
Rodriguez was placed on the 7-day injured list with Triple-A Durham due to elbow tightness, Bulls play-by-play voice Patrick Kinas reports.
Rodriguez has a 1.57 ERA, 0.70 WHIP and 22 strikeouts in 23 innings through four starts for Triple-A Durham.
Rodriguez signed a minor league contract with the Rays on Wednesday, according to Evan Petzold of the Detroit Free Press
Rodriguez cleared waivers and was outrighted to Triple-A Toledo on Thursday.
Rodriguez is serving as the 29th man for Tuesday's doubleheader against the Mariners. He is expected to pitch in Game 2.
The Tigers plan to recall Rodriguez from Triple-A Toledo to have him pitch in the second game of Tuesday's doubleheader with the Mariners, Jason Beck of MLB.com reports.