So I should have clarified my question. Shark finning has actually been banned in the US since around 1990. But as long as the fishermen don't throw the body of the shark overboard, its free game. The article that I am including at the bottom argues that if shark finning is totally abolished, it will drive the the price of shark fins up (supply and demand). Therefore, totally banning it would actually do more harm than good instead of regulating it like is done with other species of fish.
(To also clarify, I think shark finning is a completely stupid practice in which has no nutritional/medicinal value and should be banned. However, it may not be the most practical solution for our unfortunate world we live in)