Hamilton took a pitch from Boston pitcher Eduardo Rodriguez down the right field line and into the corner in the bottom of the second inning, Thursday, and received standing ovation from Rangers fans.
It was Rodriguez's major league debut.
In April, Los Angeles traded Hamilton back to Texas, where he played from 2008 through 2012, after the league chose not to suspended Hamilton in the wake of a self-reported relapse with cocaine.
He also spent the first several weeks of the 2015 rehabilitating his shoulder following surgery.
Hamilton has battled substance abuse problems throughout his career.
Hamilton signed with the division-rival Angels in December 2012 for five years and $125 million.
- Will Green