Wedding rings have been adopted as a nearly universal symbol of marriage in the western world and beyond. (However there is absolutely no requirement to exchange rings as part of a legal marriage ceremony.)
If you search the internet, you will find a wide variety of words that can be used to describe the symbolism of the wedding rings, to bless or dedicate them before they are exchanged, and of course, to accompany the moment of putting the ring on your partner’s finger.
Wedding rings are often considered to seal the vows made at a wedding, and remain as a tangible reminder of those promises.
You may want to give your ring at the same time as your promise, or to make the giving and receiving of rings an additional element of your wedding ceremony which happens after the promises have been exchanged.