Laffey, 28, has pitched for three organizations this season, most recently pitching in Triple-A with the Los Angeles Dodgers.
Signing as a minor league free agent with the New York Mets in December, Laffey made the Mets out of spring training. Laffey appeared in four games and made two starts for New York, posting a 7.20 ERA in 10 innings.
Laffey was designated for assignment April 21 and claimed off waivers by Toronto just two days later. Filling in for the injured Josh Johnson, Laffey allowed two runs in 2 2/3 innings against the Yankees on April 26.
The Blue Jays designated Laffey for assignment following the game, and he became a free agent after refusing an assignment to Triple-A Buffalo.
Laffey signed as a minor league free agent with the Dodgers on July 1. In 12 games and 11 starts for Triple-A Albuquerque, Laffey went 4-3 with a 5.61 ERA before being released.
A 16th-round draft pick of the Cleveland Indians in 2003, Laffey has a 4.45 ERA in 153 major league games with the Indians, Mariners, Yankees, Blue Jays and Mets.