You don’t specialize in law school other than to take a few electives, maybe in tax or do moot court for litigation. What will you bring to an internship? Nothing. You can run a few errands. You could watch lawyers work.
Get a job at the court house. Watch a few trials. If you are working all summer, when could you intern?
As a non-attorney you can also work as a paralegal or assist paralegals in their work. Big Law would allow this, I’m sure, as would the advocacy organizations that I mentioned earlier. Other tasks that you can fulfill are research oriented. Human Rights Now and other non-US organizatins often need native English speakers for translation work. Any of these tasks will get you up close and personal with what attorneys do.
One other organization that uses non-attorney interns and somewhat addresses human rights, although primarily domestic, is The Prisoner’s Legal Service. Some states have this organization, and so if your state doesn’t have one, you could network. Ask them what other organizations you can talk to that are similar or do other interesting work. Here’s the link to the Massachusetts PLS – http://www.plsma.org/
Here’s the NYState one – https://www.plsny.org/
How about working with Native American issues? These are autonomous territories and peoples within the US. There are any number of human rights issues in this area too. You could work directly with attorneys, with tribal leaders, with advocacy groups in DC or locally, or with the bar associations. Anything will give you insight into the issues and the tasks of attorneys on the job.
https://narf.org/nill/resources/lawyer.html