Ortega cleared waivers Friday and was sent outright to Triple-A Charlotte, Daryl Van Schouwen of the Chicago Sun-Times reports.
The White Sox designated Ortega for assignment Wednesday.
Ortega went 1-for-2 with a walk, a run scored and two stolen bases in the second game of Tuesday's doubleheader against the Nationals.
The White Sox selected Ortega's contract from Triple-A Charlotte on Friday, Daryl Van Schouwen of the Chicago Sun-Times reports.
Ortega signed a minor-league contract with the White Sox on Jan. 5.
Ortega elected to become a free agent Tuesday.
The Mets placed Ortega on outright waivers Friday, Anthony DiComo of MLB.com reports.
Ortega was added to the lineup for Wednesday's game at Miami.
Ortega is out of the lineup for Sunday's game against the Mariners.
Ortega is out of the lineup Tuesday versus the Rangers.