No, in fact no Friar or Monk is of high enough rank to have such a ring. It is Bishops and above (no matter how poor they are). Only an Abbot gets such a ring.
The ceremony, which in solemnity differs but slightly from that of a bishop’s consecration, takes place during the Holy Sacrifice of the Mass, after the Epistle. The essentials of the episcopal order are of course omitted, but before his benediction the Abbot takes the oath of allegiance to the Holy See and, like the bishop, is subjected to a canonical examination…Upon his returning to his seat in the sanctuary (if in his own church), the monks of the community come, one by one, and, kneeling before their new superior, pay him their homage, and receive from him the kiss of peace.
Here’s what they say about the kiss:
"Besides bishops, many other ecclesiastics are privileged to wear rings. The pope of course is the first of bishops, but he does not habitually wear the signet ring distinctive of the papacy and known as “the Ring of the Fisherman” (see below in this article), but usually a simple cameo, while his more magnificent pontifical rings are reserved for solemn ecclesiastical functions. Cardinals also wear rings independently of their grade in the ecclesiastical hierarchy. The ring belonging to the cardinalitial dignity is conferred by the pope himself in the consistory in which the new cardinal is named to a particular “title”. It is of small value and is set with a sapphire, while it bears on the inner side of the bezel the arms of the pope conferring it. In practice the cardinal is not required to wear habitually the ring thus presented, and he commonly prefers to use one of his own. …Abbots in the earlier Middle Ages were permitted to wear rings only by special privilege. A letter of Peter of Blois in the twelfth century (P.L., CCVII, 283) shows that at that date the wearing of a ring by an abbot was apt to be looked upon as a piece of ostentation, out in the later Pontificals the blessing and delivery of a ring formed part of the ordinary ritual for the consecration of an abbot, and this is still the case at the present day. On the other hand: there is no such ceremony indicated in the blessing of an abbess, though certain abbesses have received, or assumed, the privilege of wearing a ring of office.