At best, it may have been one of the "lesser" works of the Mirdain of Eregion which Saruman had come by.
Well, in that same encounter Saruman names himself "Saruman Ring-maker," which implies I think that the ring was one of his own creation, the fruit of his investigations into the Mirdain's craft. Nonetheless, I doubt it was a ring of much power or significance, except as an expression of Saruman's hubris.