Yes! You won’t regret it. Do some Googling to research the best policy, but you'll most likely want to look for something that covers lost rings as well as stolen ones. Also, find out how much you'll get back in the event something does happen—is it just a fraction of the price or the whole thing?
It may be "just a ring," but there's sentimental value attached to it, so in case the worst should happen, you'll be glad it's an easy-to-solve problem later on.