Catholic priests (of which Jesuits are an order) wear a ring to signify their marriage to the Church. Priests were also allowed to marry for quite some time (I don't recall exactly when that changed, but it was sometime in the 15-1600's). If you also consider the fact that Aramis (sp?) was hiding the fact that he was a Jesuit, it's not inconceivable that he would wear a ring. It's been a long time since I've read the book, but I also believe that he and Athos both were married (and widowed) in the time between "The Three Musketeers" and "Twenty Years After" (where "The Man in the Iron Mask" came from).
Yes, Catholic priests WERE allowed to get married (they were even allowed multiple wives, which was the norm at the time). They were not barred from marriage until 1022 when Pope Benedict VIII banned marriage & mistresses for priests in order to protect against inheritances of church property and the possibility of the Papacy becoming a monarchy. But enough of the history lessons, since the story takes place some 700 years after that.
I do agree with others, though, that the ring can be explained as either a "disguise" and/or the fact that Aremis was a widower.
I'm not an expert on the priesthood, but I don't think priests wore rings to signify their marriage to the church- not in the 17th century anyway, because men didn't wear wedding rings back then anyway. If they did, however, I think thering would have been slightly more ornamental than a modern neat little gold band... and if this was deliberate, why isn't he wearing it in every scene?