The 35-year-old right-hander allowed three runs -- two earned -- and six hits in five innings against San Francisco. He struck out two, walked one, hit a batter and left after 77 pitches with the score 3-3.
Jackson, who was acquired from the Oakland Athletics in exchange for cash last week, broke a tie for most teams (13) that he had shared with Octavio Dotel.
He signed a minor league contract with Oakland last month and was 1-0 with a 6.75 ERA in three games -- two at Triple-A and one at Class A. He gets paid at the rate of a $2 million salary while in the majors and can earn $500,000 in performance bonuses based on starts: $150,000 each for 15 and 18, and $200,000 for 20.
Jackson has gone 104-123 with a 4.60 ERA in 394 career games. He made his big league debut with the Los Angeles Dodgers in 2003 and also pitched for Tampa Bay, Detroit, the Chicago White Sox, Arizona, St. Louis, Washington, the Chicago Cubs, Atlanta, San Diego, Miami, Baltimore and Oakland.
He was 6-3 with a 3.33 ERA in 17 starts for the Athletics last season.
Left-hander Thomas Pannone was optioned to Triple-A Buffalo after going 1/3 with a 6.85 ERA in 14 games for the Blue Jays. Right-hander Matt Shoemaker was transferred to the 60-day injured list to open a spot on the 40-man roster.
Toronto has four starting pitchers on the injured list, including right-handers Clay Buchholz (shoulder) and Shoemaker (out for the season after knee surgery), and left-handers Ryan Borucki (elbow) and Clayton Richard (right knee).
The Associated Press contributed to this report.