The Rangers selected Curry's contract from Double-A Frisco on Friday, Joel Sherman of the New York Post reports.
Curry pitched at three different levels this season and finished with a 5.02 ERA and 1.38 WHIP across 104 total innings. The 24-year-old righty is no longer eligible to be selected in the Rule 5 Draft now that he's captured a 40-man spot, and he'll likely have a chance to capture a spot in Texas' Opening Day bullpen during spring training.