Tom,
As the others have noted, you probably won't be able to make any purchases on the Trenitalia website using a U.S.-based credit card. There have been MANY examples of that here on the HelpLine.
However, as Frank noted your card should work fine when buying tickets at the stations (unless they upgrade all the ticket machines to the newer "chip & PIN" models in the near future).
I was in a Rome and other locations in Italy a few months ago and purchased tickets on several occasions, at Termini, other stations in Italy and airports. Although my credit card is a "chip & PIN" version, the machines didn't request a PIN which means the transaction was processed using the older magnetic strip technology.
As mentioned in the previous post, it's very likely the older machines will be phased-out, perhaps even sometime this year. For those without "chip & PIN" credit cards, the options will be to use cash (some ticket machines will accept cash, some won't - keep some small bills at hand) or stand in a queue at the staffed ticket windows.
Cheers!