Kent (elbow) re-signed with the Guardians on a minor-league contract July 16 and was placed on Triple-A Columbus' 7-day injured list a day later.
The Guardians designated Kent for assignment Saturday.
The Guardians acquired Kent from the Rangers on Thursday in exchange for international bonus pool money.
Kent was optioned to Triple-A Round Rock by the Rangers on Thursday, Kennedi Landry of MLB.com reports.
Kent (oblique) struck out three and allowed one hit and no walks over three scoreless innings Saturday for Triple-A Round Rock after being reinstated from the 7-day injured list earlier in the day.
Kent (oblique) made a rehab start Saturday in the rookie-level Arizona Complex League, giving up no hits and one walk over two scoreless innings while striking out four.
Kent is on the 7-day injured list at Triple-A Round Rock with a strained oblique, Evan Grant of The Dallas Morning News reports.