Absolutely, although its origins are African. In fact Thomas Jefferson observes that slaves played an instrument that he called the “banjar”. Today there really is no instrument that is more associated exclusively with American music than the banjo.
I’d agree about the dobro as well, but since it’s not very well-known. (ask your non-instrument-playing friends if they know what a dobro is) I don’t think it qualifies. Just my $0.02, though.