In addition, Colby Lewis, who was pulled from his last start with forearm stiffness, did not throw today, and his start on Tuesday is in doubt. If Lewis can't go, the Rangers will bring Martin Perez up from AAA to take his start.
The situation with both Oswalt and Lewis is still up in the air, and it is possible one or both of the pitchers could end up on the disabled list. Unless both of them are expected to miss significant time, however, I would not anticipate the Rangers making a move for a starting pitcher (other than Cole Hamels or Zack Greinke, who the Rangers are interested in regardless).
The Rangers are currently up six games in the A.L. West. Neftali Feliz will likely be ready to return to the major league rotation after two more rehab starts. The Rangers seem comfortable with the idea of Martin Perez making a spot start, as needed.
Things would change if more pitchers get hurt, or if Oswalt or Lewis are done for the season, but right now, I can't imagine that the Rangers are going to make a panic move to go get someone like Wandy Rodriguez or Ryan Dempster as a band-aid.