Dozens of internships are available, and some are directly related to archives and/or records management. Please find the list on this PDF.
Frankfort, KY: Archivist I, Kentucky Department for Libraries and Archives
Pasadena, CA: Head of Archives & Special Collections, California Institute of Technology
Bismarck, ND: Electronic Records Archivist, Historical Society of North Dakota
New Haven, CT: Lead Administrator 2, Yale University Beinecke Library
Charleston, SC: Project Digitization & Metadata Specialist, College of Charleston
Thanks to Aaron for this one!
Cleveland, OH: Archivist, University Hospitals
Ithaca, NY: Collections Specialist, Cornell University Roper Center
South San Francisco, CA: Corporate Archivist (short term), Genentech
Baton Rouge, LA: General Librarian (Metadata), Louisiana State University
Thanks to Tara for this one!