Department of State Student Internship Program Act This bill requires the Department of State to establish the Department of State Student Internship Program to offer paid internship opportunities at the State Department to raise awareness of the role of diplomacy in the conduct of U.S. foreign policy. Participants must be enrolled at an institution of higher education (IHE) and able to receive and hold an appropriate security clearance. The State Department must pay participating interns a specified amount, as well as provide housing and travel assistance. The State Department may also enter agreements with IHEs to ensure these internships satisfy criteria for the academic programs in which participants are enrolled. Additionally, the State Department must transition all of its unpaid internship programs to internship programs that offer compensation.