Immigrant Veterans Eligibility Tracking System Act or the I-VETS Act This bill directs the Department of Homeland Security (DHS), upon an alien's application for an immigration benefit or the placement of such alien in an immigration enforcement proceeding, to: determine if the alien is serving, or has served, as a member of a regular or reserve component of the Armed Forces on active duty or as a member of a reserve component in an active status; and annotate every DHS immigration and naturalization record relating to such an alien to reflect such membership and to afford an opportunity to track the outcomes for each alien.