Do American universities accept a one-year MSc?

It depends upon the discipline, but in many cases, students in the U.S. are able to begin a Ph.D. program directly from undergraduate studies, so the length of your MSc would be irrelevant to your being admitted to a doctoral program. In some fields, students are required to complete a master's degree along the way if they don't already have one, and I believe that your completed degree would be acceptable to fulfill that requirement in most cases.