Ignore what you've read about U.S./British differences in tense usage. It's not as clear as they say. You don't need to change your English to speak to U.S. speakers. Here in the U.S. we understand both effortlessly and we use both. We use the present perfect often. We hear it and read it all the time.
We are just a little more likely to _say_ "I told him" than "I've told him," or "I went to the store" instead of "I've gone to the store."
A few examples of U.S. use of the present perfect I just found.
(A few examples of U.S. use of the present perfect I've just found.)
“I have told her to take some time to relax and rest,” said Steve Duprey, an Ayotte backer and member of the Republican National Committee.
"I have told Ryan that I can't sleep or eat because he's always on my mind."
Christie this week said he has “every intention of serving out my full term as governor. “I’ve said that from the beginning,” Christie said.
Here's an interesting example in which the Governor of Massachusetts uses both in the same sentence. I don't think there's any difference in meaning at all, he just happened to say it both ways:
“I said that the president has made clear he wants to unify the country post-election, and I’ve said that based on Bannon’s previous remarks and activities that was a concern to me,”