The former American League most valuable player is recovering from shoulder surgery Feb. 4 and had been working in the Rangers' extended spring program in Arizona since April 28.
Hamilton left after five innings.
Before the game, Hamilton spoke about his return to baseball.
"It's really a small miracle that I got back here because it was a whole, big, long, ugly process," Hamilton said. "I feel like the Lord had his hand on it to get me back here. I feel like I'm in the place I'm supposed to be in now."
Hamilton said he's trying to be open and honest, and hopes people understand he doesn't want to hide behind his mistakes.
He self-reported a cocaine and alcohol relapse during the off-season. That led the Angels to trade Hamilton to the Rangers on April 27.
"The last couple years obviously haven't been what I wanted them to be as a player," he said. "I haven't been that guy. It wasn't like I didn't try to put the work in and be that guy. But there were some distractions away from the field, and those are being resolved."
Detroit Tigers left-hander David Price's next start is being pushed back to Saturday while he recovers from a right hamstring strain.
Price was injured Friday night when he stepped on a bat that had been tossed aside by an umpire in anticipation of a possible play at the plate.
Tigers right-hander Justin Verlander, who has been sidelined all season because of a strained triceps, threw off flat ground and said he might be ready for a light bullpen session Tuesday.
Red Sox shake up roster
The Boston Red Sox are shaking up their roster, recalling outfielder Jackie Bradley Jr. and right-hander Steven Wright from triple-A Pawtucket and optioning outfielder Allen Craig and right-hander Robbie Ross to Pawtucket.
Bradley Jr. was batting .343 with one home run and nine runs batted in at Pawtucket, and Wright was 2-1 with a 3.24 earned-run average in four starts.
Craig was batting .135 with one home run and two RBIs in 24 games, and Ross had no record and a 6.17 ERA in 13 relief appearances.
The Toronto Blue Jays put outfielder Michael Saunders on the 15-day disabled list because of inflammation in the left knee and selected utility player Steve Tolleson from triple-A Buffalo.
Saunders had surgery in spring training for torn cartilage and didn't make his debut until April 25. He is batting .194 with no home runs and three RBIs.
To make room for Tolleson, the Blue Jays designated minor league right-hander Preston Guilmet for assignment.