There's no timetable on when Davis, who is coming back from elbow surgery, will join the big league team. Davis can opt out of his contract if he's not brought up to the majors by May 30. If he is brought up to the majors, his base salary is $900,000.
Davis, 35, yielded two singles and two walks while striking out seven.
"Everything felt pretty good," Davis told MLB.com. "The release point on all my pitches was good. My arm felt great, my body felt good.
"It feels like I can really let the ball go without having to worry about some tingling feeling or numbness in my pinky or ring finger. To be able to go out there and snap my curveball with all my strength makes pitching fun and easier as well."
ESPNChicago.com's Bruce Levine contributed to this report.