I don't think it's a fern... off the cuff, I'd say it closely resembles a Clematis, but I say that very tentatively.
I hate to be contrary, but it most probably is the Japanese climbing fern, Lygodium japonicum, a weedy species in parts of the American south. There is an excellent webpage here from the Archbold Biological Station in Lake Placid, Florida that shows the incredible variation in the leaves of this species. Note the venation visible on this superb image; it shows simple, non-reticulate veins typical of many ferns. The position of the leaf blades is somewhat confusing, in that they appear to be oppositely arranged (hence the similarity to clematis); however, the leaves themselves, which arise alternately from the stipe (stem) are composed of various pinnae (divisions), and these are arranged bilaterally, at least on this part of the stipe.
