Yes you would need an FAA licence.
Now on the other hand you could go as a "tourist" to the warbird museum at Kissimmee Airport, South Orlando.
They have Harvard rides, Waco Bi-plane rides etc... great fun!!!
Just let the pilot know that you fly at home... probably get a go that way. :-)
I had a ride in the Waco there, but that was back in '92 when I was only 15.