Oakland marks Jackson's 13th major league team, matching former reliever Octavio Dotel's record.
After going 5-6 with a 5.21 ERA for Baltimore and Washington last season, Jackson had spent this season in the Nationals' system without pitching in the majors. The 34-year-old right-hander opted out with Washington, then signed a minor league deal with the A's on June 6.
He had been slated to start for Triple-A Nashville on Monday, the San Francisco Chronicle reported. Jackson is 0-1 with a 4.02 ERA in three starts for the Sounds, having allowed 12 hits and eight walks in 15⅔ innings while striking out 16.
Jackson has started 288 of his 377 career major league games since his debut in September 2003 with the Los Angeles Dodgers. He has a 98-120 record with a 4.67 ERA.
The injury-ravaged A's rotation has five starters on the disabled list: Trevor Cahill (Achilles tendon strain), Daniel Gossett (elbow strain), Brett Anderson (shoulder strain), Andrew Triggs (nerve irritation in arm) and Jharel Cotton, who is done for the season after undergoing Tommy John surgery.
The Associated Press contributed to this report.