No. Law schools do not require that applicants have an internship or experience in a legal setting. Most legal internships are designed for law students who have learned how to research and write like lawyer. The greatest value in legal internships for undergraduates is obtaining a realistic view of the practice of law that will help you decide whether to attend law school. You can gain this experience through informational interviewing, shadowing attorneys, participating in mentoring programs and observing court sessions.
Here are some additional resources at Penn State for your internship search: