Shama-il Tirmidhi Chapter 012, Hadith Number 003 (092).

It is related from Hazrat Abdullah bin Ja'far radiyallahu anhu from another source (another chain of narrators) that the Prophet of Allah sallallahu alaihe wasallam wore a ring on the right hand.

Commentary.
In a hadith it has also been stated that beauty and elegance is more appropriate to the right hand. Therefore Ibn Hajar, who is an Imam of the science of hadith says, "After studying that hadith, I have found that if it is worn for elegance and beauty, it should be worn on the right hand, and if it is worn for use as a seal or stamp it should be worn on the left hand, as it is easier to remove from the left hand when using it."

It is mentioned in the ahaadith that the ring was worn on both hands (right and left).