Annoying nitpick: There was not one Ring of Power, but many, and the one Frodo carried to Mordor is known as the One Ring, the only one forged by Sauron himself. Nine other Rings of Power were carried into Mordor by the Nazgûl, the Ring-wraiths, when they were corrupted by the power of Sauron in the Second Age (though they did not wear the Rings anymore in the Third Age). Three of the Seven Dwarven Rings were also acquired by Sauron, and they will have been brought to Mordor by someone, possibly Sauron himself (when he fled Dol Guldur in TA 2941, he likely brought at least the Ring of Thrór to Mordor).
I got finger by accident somehow, I think cuz for The Ring I was just guessing random cursed objects and finger came to mind even though now I remember it was a video
eta - just googled it and see now that I'm wrong, which is sad.