Any Catholic wedding is subject to laws of the country or state. In the United States, the priest or deacon actually signs the civil license as well as the marriage license so it's done simultaneously.
That's pretty much the case everywhere. Were you to get married outside the country, you would provide documentation to the priest, including your baptismal records from the United States.
I don't know what the process is but they might insist on making sure it's registered in the United States as well since you're an American citizen. You will probably run into a mountain of paperwork. They are going to want to know why you want to get married and they may want proof that you're not already legally married in the United States.
If you're doing this so the marriage won't affect any government benefit you're receiving, which some try to do, it's considered fraud.
I'm sure it's possible to get married in the Church outside in another country but I frankly don't know of any country where you wouldn't need some civil component and, as I said, they might require that it be reported in the country where you're a citizen and where you reside.