The Rangers said Hamilton is set to move up from extended spring training this weekend. He went 1 for 5 with a three-run homer while playing five innings in left field Friday against Seattle minor leaguers.
The 34-year-old Hamilton has been on the 15-day disabled list while recovering from right shoulder surgery on Feb. 4.
Texas reacquired the former AL MVP and received cash from the Los Angeles Angels on April 27 for a player to be named or cash.
''I believe that he'll be able to tell us when he's ready,'' Rangers manager Jeff Banister said before Friday night's game at Tampa Bay.
''How many at-bats this is, we'll all evaluate that, with him involved. I think it's about him being in shape, his legs underneath him, his ability to repeat daily, how he feels after nine innings,'' he said.