Getting through Tuesday's session is a sign that Rodriguez should be ready to go on Friday against the Indians.
"Very good ... no problems," Rodriguez said. "It is feeling better. I feel good enough to throw."
Rodriguez, who was signed as a Minor League free agent at the end of Spring Training, is 1-1 with a 2.70 ERA in four starts. But injuries have plagued him the last two seasons. He made just 12 starts for the Pirates in 2013 before suffering a season-ending forearm injury. He made just six starts for the Pirates last season while dealing with inflammation in his right knee and was released on June 1. Rodriguez is 36 years old.
• Matt Harrison, who underwent spinal fusion surgery on June 3, 2014, is scheduled to throw in an extended Spring Training game in Arizona on Wednesday. Harrison has been throwing in the bullpen and live batting practice, but this will be his first outing under simulated game situations.
• Derek Holland, who has been sidelined since his first start with a strained left shoulder, is awaiting clearance to throw. Holland was examined last Friday and was told that the injury was not quite completely healed. He'll have another exam a week from Friday to see if he is ready to begin a throwing program.
• The Rangers aren't scheduled to face American League Cy Young Award winner Corey Kluber this weekend during their three-game series against the Indians. He's slated to pitch on Wednesday against the Cardinals. The Indians are tentatively scheduled to go with Danny Salazar, Bruce Chen and Carlos Carrasco.
T.R. Sullivan is a reporter for MLB.com. Read his blog, Postcards from Elysian Fields, follow him on Twitter @Sullivan_Ranger and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.