The gemara (Shabbat 62) allows a man to wear a signet ring in reshut harabbim, as it is common for men to wear those. Other rings, however, are not normally worn by men, and they thus cannot be considered a garment. Wearing such rings thus constitutes carrying, rather than wearing, and is forbidden in a public domain on Shabbat (OC 301:9).
While a man’s wedding ring is probably not to be considered beged isha, it still conveys an effeminate spirit, in my opinion, and portrays marriage in a light inimical to classic Jewish understandings of matrimony.