Vaccine Administration Centralization to Coordinate and Improve National Execution Act or the VACCINE Act This bill establishes a grant program for states, tribal nations, and territories to set up or expand COVID-19 (i.e., coronavirus disease 2019) vaccine registration systems. The system must be the jurisdiction's sole means of registering an individual for a vaccine. The Department of Health and Human Services (HHS) must set up a website and a call center to share information with the public about each registration system. HHS must also develop standards to allow for electronic information exchange among the systems. To carry out the program, HHS may use funds from the Public Health Emergency Fund. The authority for this program terminates at the end of the COVID-19 emergency period.