The Rangers designated Burke for assignment Sunday.
The transaction opens up a spot on the 40-man roster and in the big-league bullpen for right-hander Matt Festa, who was called up from Triple-A Round Rock. Since breaking his right hand in April and missing two months of action, Burke struggled to bounce back upon returning from the shelf. Over his eight appearances with Texas since being activated, Burke posted a 7.59 ERA and 1.88 WHIP across 10.2 innings.