Anulus is the nominative singular while anulos is the accusative plural. We are talking about one ring so we have to use a singular form and the verb placet is being 'performed' by anulus. The translation would more literally "Is my ring pleasing to you?"
Look at the plurality of the subject (here anulus meus). Since it is singular we use placet (singular third person) with -ne appended. If the subject was anuli mei then we would use placent (plural third person) with -ne appended.