Ramos agreed to a deal Tuesday with the Long Island Ducks of the independent Atlantic League.
The Rangers released Ramos on Sept. 10.
Ramos signed a minor-league contract with the Rangers on Tuesday and was assigned to Triple-A Round Rock.
Ramos underwent surgery to repair his torn ACL on Wednesday, James Wagner of The New York Times reports.
Ramos (knee) was placed on the injured list Tuesday, Mandy Bell of MLB.com reports.
Ramos suffered a torn ACL and sprained MCL in Sunday's win over the Red Sox, Mandy Bell of MLB.com reports.
Ramos went 1-for-3 with a two-run home run and a walk in Monday's 9-3 win over Cincinnati.
Ramos went 3-for-4 with a solo home run and a pair of singles in Saturday's 2-1 loss to the Tigers.
Ramos' contract was selected by Cleveland on Friday, Mandy Bell of MLB.com reports.
The Tigers requested unconditional release waivers on Ramos (back) on Sunday.