Robinson is out of the lineup for Monday's game against the Orioles.
The White Sox recalled Robinson from Triple-A Charlotte on Friday.
The White Sox selected Robinson's contract and optioned him to Triple-A Charlotte on Sunday.
Robinson signed a minor-league contract with the White Sox on Dec. 7.
Robinson elected free agency Tuesday, Charlie Goldsmith of The Cincinnati Enquirer reports.
Robinson signed a minor-league contract with the Reds on Monday, which includes an invitation to spring training, Bobby Nightengale of The Cincinnati Enquirer reports.
Robinson cleared waivers and was outrighted to Triple-A Louisville on Friday.
Robinson isn't starting Tuesday's game versus the Cardinals.