GI Internship Program Act This bill requires the Department of Veterans Affairs (VA) to establish a program to match veterans who are entitled to educational assistance with internships to provide such veterans with work experience and marketable skills. The VA shall establish criteria that employers must meet to participate in the program. The following employers are excluded from participating in the program: (1) government agencies, (2) employers who cannot provide the VA with certain assurances, and (3) employers who have previously participated in the program and failed to abide by its requirements. The VA shall pay individuals who are full-time participants in such an internship the amount of educational assistance payable to those participating in a full-time apprenticeship or other on-job training programs. Interns shall be considered as employees of the VA, not the program employer, for purposes of the Patient Protection and Affordable Care Act. Additionally, each intern and employer shall provide the VA with a monthly certification that the intern worked at least 35 hours each week performing functions that provided the individual with valuable experience. The VA and the Department of Labor shall create and publicize a website to serve as a portal for the program. The VA shall (1) minimize the administrative burdens incurred by employers due to their participation in the program, and (2) ensure that employer participation is at no cost to the employer.