The United States government tightly regulates the employment (and internships) of foreign nationals, so the answer depends on the type of visa the student has. The student must have either an F-1 or J-1 visa. One benefit of the F-1 and J-1 status is that most students may apply for work authorization to accept a variety of employment opportunities. Best of all, it is possible for students to begin working without their employers having to provide visa sponsorship. Working in the US without prior authorization is a serious violation of immigration regulations and may lead to cancellation of the student's visa. For more information about F-1 Visas, see here. For more information about J-1 visas, see here. Several institutions of higher education have posted guides for employers who want to hire international students as interns:
University of Michigan, U.S. Employer's Guide to Hiring International Students University of Chicago, Employer Guide for Hiring International Students Northwestern University, Employer Guide: Hiring International Students