While principally supporting students and academic lecturers/researchers, the Fulbright Program does also support artistic exchange under its Foreign Student Program, which 'offers opportunities for foreign graduate students, young professionals and artists from abroad to study and conduct research' within the United States.
The one universal requirement is that applicants must have completed undergraduate education and hold a degree equivalent to a bachelor's degree, and then further eligibility requirements can be set by individual countries participating in the Program.
For more details on the Program and on how to apply see the Fulbright site. Note that applications are made through national branches of the program (see here for list), and that these establish yearly deadlines.