The Rangers reinstated Burke (hand) from the 60-day injured list Wednesday.
Burke has been on the injured list since mid-April with a broken right (non-throwing) hand. He began a rehab assignment May 16, posting a 2.45 ERA and 1.09 WHIP through 11 innings across nine appearances -- seven of which came in Triple-A. The left-hander will presumably slide into a middle relief role with the Rangers, and his return will push Grant Anderson back to Triple-A Round Rock.