Yes. However, dual citizens of the U.S. and Japan must renounce their Japanese citizenship before departing for Japan if accepted. Japanese law requires that individuals choose either Japanese nationality or their other nationality. To apply for the JET Program, you must prove that you have U.S. nationality, therefore it is not possible to also hold Japanese nationality as a JET participant.
If you have dual nationality with the United States and another country, this does not affect your eligibility for the JET Program, however, if you have nationality with another country that also participates on the JET Program (such as Canada, Australia, etc.) you can only apply through ONE of these countries.