Kelly has been suspended one year for violating Major League Baseball's gambling policy, Jared Diamond of the Wall Street Journal reports.
Kelly (3-2) picked up the win over Atlanta on Saturday, firing a scoreless inning during which he issued two walks and uncorked a wild pitch.
Kelly (2-2) took the loss against the Rays on Wednesday, allowing an earned run on two hits over one-third of an inning.
Kelly (2-1) took the extra-inning loss against the Astros on Tuesday, allowing an unearned run on one hit over one-third of an inning.
Kelly (1-0) got the win Tuesday against the Rangers, firing a perfect eighth inning.
The Athletics claimed Kelly off waivers from the Guardians on Friday.
Kelly was designated for assignment by the Guardians on Tuesday.
Kelly was optioned to Triple-A Columbus on Sunday.
The Guardians recalled Kelly from Triple-A Columbus on Saturday, Mandy Bell of MLB.com reports.
Cleveland optioned Kelly to Triple-A Columbus on Thursday.