Jackson signed a minor-league contract with the Giants on Friday, Maria I. Guardado of MLB.com reports.
The 33-year-old began the 2020 campaign in Japan but returned to affiliated ball with the Reds in August on a minor-league deal. Jackson last appeared in the majors with the Brewers in 2019 and posted a 4.45 ERA, 1.32 WHIP and 47:18 K:BB over 30.1 innings.