This small item is not a ring, but a Woggle. (though it is shown on a finger) A woggle is a little-known item used to gather up a cloth tie. The tie is usually worn on the neck or shoulders of a human. They're most known in scouting (boyscouts/girlscouts) but other uniforms can use them too. It gathers the tie together. Most often they are woven items, or carvings. They usually have a little stem on one side (in this case, it's a blue arm giving the "3" sign, which is the Scout Sign / Scout Salute) which differentiates them from ordinary rings or loops. It is highly curious that such a specific item would have a Sonic theme. 

Additional Woggle Info:
The Scouting Movement teamed up with Sega back in 1993 and launched "The Sonic Challenge". It involved selling scratch cards to raise money for The Promise Appeal, to help The scout Movement. Cubs and Scouts could also take part in a Sonic Speed Challenge within their local groups to set new time records on typical Scouting activities like putting up tents, lighting camp fires, tying knots and running relays. Anyone who participated in the event got this woggle as a prize."