Can I house a carpet python in an exo terra terrarium?

That is barely large enough for a 4 ft. carpet. I keep my chondros in 3ft X 2 ft X 2 ft cages and I'd prefer larger if I could. Being partially arboreal, carpets really should be in cages longer than wider. A minimum 4 ft cage is necessary as your carpet will outgrow one as small as that exo terra in no time. The other issue is that the exo terra's having screen tops, don't hold humidity well enough to keep carpets in. You'd have to partially cover the top with plastic or use a heat panel that covers most of the lid to keep in the heat and humidity. They are not my first choice for arboreal and semi-arboreal tropical species.

That's a bit cramped already, and you're barely going to keep it for a year in it, though I don't even think you should put it in there. It'd be much better in a larger environment. That said, use jungles vines like these http://lllreptile.com/store/catalog/reptile-suppli... They're big enough that you can twist wrap two them together and it could easily hold a snake twice yours size.

Maybe a year or two.