Rayon can be produced in a variety of ways and in a variety of forms. Regular rayon (viscose rayon) is produced in the U.S. Cupranomium rayon, which is similar to viscose rayon, is not produced in the U.S. because of its effects on the environment but it is still produced in Italy.
http://en.wikipedia.org/wiki/Rayon
http://www.museumtextiles.com/1/category/rayon/1.html