Ogando, 29, returned from the disabled list at the beginning of the month, but has pitched only in relief in four appearances since then. He's allowed just one hit and struck out five in six scoreless frames in that span.
The tall right-hander, who has battled with shoulder woes for much of the year, will go only three or four innings on Tuesday before handing the reins over to the bullpen, per Jeff Wilson of the Fort Worth Star-Telegram.
In his bid to stop the Rangers' skid at seven games, Ogando will oppose Rays right-hander Jeremy Hellickson, who also hasn't seen much big-league action recently. Hellickson, 26, is making just his second start since returning from a brief stint in the minors.
Ogando owns a 3.47 earned-run average in 15 starts for the Rangers this season, while Hellickson has a 5.04 ERA in 29 outings.
If the Rangers win Tuesday, they will pull even with the Rays in the AL Wild Card race. A loss coupled with an Indians win will put the club a half game out of a playoff spot.