Got into an interesting conversation with a friend about this, and neither of us were quite sure as to what the actual effect of the ring would have on someone if they were already underwater.
Nothing, unless you choose to swim to the surface.
The description of the Ring of Water Walking states:
While wearing this ring, you can stand on and move across any liquid surface as if it were solid ground.
It simply gives you the ability to walk on the surface of water as if it were solid ground. It doesn't force you to do anything, and doesn't force anything to happen to you. Since you're underwater, there's no liquid surface to walk on from your present position.
Of course, you can swim to the surface of the water. From that point, you would be able to stand on and move on the surface of the water as if it were solid ground.