Maine appeared in 30 games for the Cubs and Indians last season, while posting a 6.07 ERA. The 27-year-old also pitched in 30 games at the Triple-A level, and went 4-2 with a 2.72 ERA.
The Blue Jays have now made six claims this month, with the main goal of acquiring some players through waivers in order to build depth at the Minor League level.
Toronto also announced on Wednesday that Kyle Drabek, Drew Hutchison, Dustin McGowan, Sergio Santos, J.A. Happ and Luis Perez were all activated from the 60-day disabled list. Santos and Happ are the only pitchers from that group that are expected to be ready for the start of Spring Training.
In order to make room on the 40-man roster, outfielder Scott Cousins and right-hander David Herndon were designated for assignment by the club. Toronto currently doesn't have any openings on its 40-man roster, but that is expected to change in the near future.
Cousins was claimed off waivers from the Marlins earlier this month, and has batted .183 with nine RBIs in 175 career at-bats at the big league level. If no team puts in a claim, the Blue Jays would be able to outright Cousins to Triple-A Buffalo.
Herndon was also claimed earlier this month, after allowing four earned runs in 7 2/3 innings in Philadelphia last season. The 27-year-old is coming off Tommy John surgery and is not expected to be available until at least June.