Do you happen to know if the ring is pure silver or alloyed with any other metals? Gold, silver, and platinum are considered "noble metals" because they are so chemically inert. Biologically, they are pretty safe and non-toxic. They typically pass through the body unchanged and do not get absorbed. However, gold and silvers are also very soft, so when used for decoration, pure gold or silver would bend or scuff easily. For this reason, most jewelry is made from metal alloys. For example, sterling silver, is an alloy of silver and a harder metal, usually copper - 92.5% silver, 7.5% copper to be exact. If you are not sure if a ring is sterling silver, look for an engraving of 925 on the inner band. Copper poisoning in birds is rare, although it can happen if they eat enough of it. The small quantity available in sterling silver is unlikely to be enough to do harm, unless the bird eats a whole lot of it. But it is also possible for sterling silver to be made by alloying with other heavy metals, like zinc.
Zinc is QUITE toxic to birds. Even a small amount might be enough to cause harm, especially if the bird swallowed a piece of the metal or chewed on it regularly for a long time, like if a bell made from a zinc alloy was on its favorite toy. Lead is also very toxic to birds, but since it is very toxic to people too, it is less likely to be found in jewelry that is purchased from a reputable source. But even jewelry from a good source might be made by questionable methods, so just something to be aware of. Also, it is important to be aware that some rings, especially cheap ones, might be silver-plated instead of being solid silver. This means that the ring is made from a less expensive metal with a silver coating on it. The underlying metal might not be safe, so if the bird chewed through the plating, it might ingest something harmful.
Basically, if it is a very expensive ring, your parrot would probably be safe to chew it. But if it is a cheap ring, it might not be safe.
Yes, parrots have expensive tastes. But we already knew that.
