Religious Worker Visa Reciprocity Act of 2017 This bill amends the Immigration and Nationality Act to prohibit, as of October 1, 2017, the Department of Homeland Security (DHS) from approving a petition for classification of an alien as a special immigrant religious worker/minister if DHS has determined that the alien's country of nationality: is identified as a Country of Particular Concern or a country where religious freedom is of significant interest in the 2013 International Religious Freedom Report, or does not extend reciprocal immigration treatment to U.S. nationals who are seeking resident status in order to work in a religious vocation or occupation.