No, it won't repair itself. I've had this happen to some of my cacti, and I just leave it alone. Cacti in their natural environment are rarely, if ever, perfect. Sometimes, I place an interesting rock or piece of wood on the damaged side of the cactus, to make the wound less obvious.
You certainly could
cut off the top of the cactus, allow it to dry, and replant it, if that's what you want to do. I'd wait until the part of the cactus above the damaged area had grown a bit taller, but the choice is entirely yours. Save the bottom section of the cactus, because it will probably produce offsets, which can be potted up individually, too. They make nice gifts for friends.
"Isn't it enough to see that a garden is beautiful without having to believe that there are fairies at the bottom of it too?" - Douglas Adams