-R Visa
Religious workers may apply for an "R" visa which is normally good for 3 years.

Religious workers are defined as foreigners coming to the United States solely to work for a bona fide nonprofit religious organization or denomination.

You may qualify for this type of visa if the purpose of your trip is to work either as a minister of religion, or at the request of the organization or affiliated organization in a religious vocation or occupation, whether in a professional capacity or not.