Each semester, there are hundreds of internship opportunities with individual members of Congress and committees. The listings are updated each week so there are always new positions being listed. The most recent internship bulletin for the House of Representatives is attached to this post.
If you would like to sign up to receive the House's bulletin in your email inbox each week, go to https://www.house.gov/employment/positions-with-members-and-committees/subscribe-to-the-house-employment-bulletin.
For information on internships with the Senate, go to https://www.senate.gov/employment/po/internships.htm.