Illegal to keep? No.
Illegal to catch yourself without proper permits? Yes.
Sharks in us water are federally protected under 36" long. Above that size, you can catch them and kill them, but you will need a permit to keep them alive. Alos be careful b/c some places require a seperate permit to transport a native animal that is wild caught as well.
But I won't say it's not possible. I've been granted several permits to collect and transport sharks in US waters. Usually you have to prove that you have the proper set up to collect, transport and hold them long term.
Another thing to consider is that you will need a large enough quarantine area to properly house the shark until it goes to the end tank.