Immigrant Veterans Eligibility Tracking System (I-VETS) Act This bill directs the Department of Homeland Security (DHS) to: identify aliens, when they apply for an immigration benefit or are placed in an immigration enforcement proceeding, who are serving, or have 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 all DHS immigration and naturalization records relating to an identified alien to reflect such identification and afford an opportunity to track the outcomes for such aliens.