The Royals re-signed Cox to a minor-league contract Tuesday.
Cox opted out of his minor-league deal to become a free agent Thursday, Mark Feinsand of MLB.com reports.
Cox (knee) was activated from the 7-day injured list Tuesday and reassigned to Double-A Northwest Arkansas.
Cox (knee) signed a minor-league contract with the Royals on Saturday.
The Royals designated Cox (knee) for assignment on Friday.
Cox was diagnosed Tuesday with a full ACL tear as well as damage to the MCL in his left knee, Anne Rogers of MLB.com reports.
Cox was placed on the 60-day injured list with a sprained left knee Saturday.
Cox retired one batter and picked up his third hold of the season but was charged with two earned runs on two walks in Monday's 7-6 win over the Royals.
Cox was recalled from Triple-A Omaha on Wednesday.
Cox was optioned to Triple-A Omaha on Tuesday.