there are two ways to go about getting your U.S. ATP:
get a U.S. private pilot certificate based on a foreign license. you will need to take an abbreviated instrument written. with this, get three hours test prep, pass the commercial written, and take the commercial pilot practical examination. with this, take the ATP written, and take the ATP practical examination.
the second method is far easier; take the ATP written and take the ATP practical exam using your foreign ATP as basis. the only problem with this route is that the A320 type will not transfer.
it will transfer on to the private based on a foreign, and then transfer to the commercial, and then to the ATP. so more convoluted route, but you obviously want to keep the type rating.
i guess there is one other method, and that would be to take an A320 type ride in a 142 school (flight safety, CAE, simuflight, etc.), and also have them issue you an ATP certificate, again basing it on your foreign ATP.
so, yeah, i guess there are three ways you can get the US ATP, but only two will have the A320 type on it. i would assume that my last suggestion is cost prohibitive.
check with your local FSDO to confirm.