GI Internship Program Act - Directs the Secretary of Veterans Affairs (VA) to establish a career transition internship program to match individuals who are eligible for veterans' educational assistance with employers to: (1) provide such individuals with work experience in the civilian sector, (2) address the growing skills gap in the U.S. economy, (3) increase the marketable skills of such individuals, and (4) assist such individuals in obtaining long-term employment.

Requires the Secretary to establish criteria employers must meet to participate in the program. Excludes as program employers: (1) federal, state, and local government agencies; (2) employers who cannot provide the Secretary with certain assurances, including their intention to retain interns after their internship ends; and (3) employers that have previously participated in the program and failed to abide by its requirements.

Directs the Secretary to pay individuals who are full-time participants in such an internship the amount of educational assistance they are due.

Requires each internship to last for at least 180 days but for no more than one year.

Considers each intern to be an employee of the VA for purposes of the Patient Protection and Affordable Care Act.

Requires each intern and employer to provide the Secretary with a monthly certification that the intern worked at least 35 hours each week performing functions that provided the individual with valuable experience.

Directs the Secretary and the Secretary of Labor to create and publicize an Internet website to serve as a portal for eligible individuals and employers to learn about the program and apply. Allows individuals to apply within 180 days of their expected discharge or release from the Armed Forces.

Directs the VA Secretary to minimize the administrative burdens incurred by employers due to their participation in the program and ensure that employer participation is at no cost to the employer.