Martin, 26, has gone 20-14 with a 3.31 ERA in 139 appearances (four starts) in four Minor League seasons. He posted an 8-1 record with a 2.27 ERA and 80 strikeouts in 44 appearances with Double-A Akron last year.
The Indians selected the Samford University product in the 10th round of the 2012 Draft.
Andrew Astleford is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.