Manager Jeff Banister said right-hander Phil Klein and left-hander Cesar Ramos are still in the mix as well, even though they haven't been given the prime innings or starts in a Cactus League game.
• Spring Training information
"We have time to get them ready if needed," Banister said.
Gonzalez, the club's first-round Draft pick in 2013, got the news after throwing five scoreless innings against the Reds on Thursday, although he walked three. Gonzalez had a 4.73 ERA in four Cactus League outings, with opponents batting .260 against him. But he walked seven in 13 1/3 innings and struck out two.
"When you watch yesterday's game, that's kind of where Chi Chi needs to be consistently," Banister said. "The ability to throw strikes to the low part of the zone. I felt the slider and the curveball were sharp. The changeup was a little firm, it needs more separation. It's about consistency of strikes and executing pitches. Chi Chi understands that."
Gonzalez was 4-6 with a 3.90 ERA in 10 starts and four relief appearances in his first and only season for the Rangers. He walked 32 batters and struck out 30 in 67 innings. Gonzalez was the only American League pitcher with at least 60 innings to issue more walks than strikeouts.
"My message to Chi Chi is it's not about being the fifth starter, it's being one of the starters," Banister said. "It's an opportunity for Chi Chi to go work and be ready when needed. He is going to pitch some significant innings for us. It's best he go get ready."
The Rangers also reassigned pitcher Nick Tepesch to Minor League games. Tepesch made 39 starts for Texas in 2013-14, but he missed all of last season because of thoracic outlet syndrome in his right shoulder.
"Tepesch is coming off an injury year," Banister said. "I felt like he knew he was on the outside looking in for the fifth spot. He still competed well. He feels good. We urged him to continue to build up and work."
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.