The 25-year-old Roach has made 17 career appearances in the Major Leagues, including two starts. He was originally drafted in the third round of the 2010 Draft by the Angels and has since played for the Padres, the Cubs and the Angels.
Toronto placed outfielder Michael Saunders on the 60-day disabled list to make room for Roach on the 40-man roster. Saunders was previously ruled out for the season because of a bone bruise in his left knee.
Gregor Chisholm is a reporter for MLB.com. Read his blog, North of the Border, follow him on Twitter @gregorMLB and Facebook, and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.