Responsible Electronics Recycling Act - Amends the Solid Waste Disposal Act to: (1) prohibit the export of restricted electronic waste to countries that are not members of the Organization for Economic Cooperation and Development (OECD) or the European Union (EU), or Liechtenstein; (2) require the Administrator of the Environmental Protection Agency (EPA) to develop and promulgate procedures for identifying certain electronic equipment as well as additional restricted toxic materials contained in such equipment which poses a potential hazard to human health or the environment; and (3) establish criminal penalties for knowingly exporting restricted electronic waste in violation of this Act. Allows certain exceptions to such export ban.

Defines "restricted electronic waste" to include electronic equipment (excluding parts of a motor vehicle), such as computers, televisions, printers, copiers, video game systems, telephones, and similar used electronic products, that contain cathode ray tubes, batteries, switches, and other parts containing lead, cadmium, mercury, organic solvents, hexavalent chromium, beryllium, or other toxic ingredients.

Requires persons who handle restricted electronic wastes to permit appropriate EPA and state officials access to such wastes upon request.

Directs the Secretary of Energy to establish a competitive research application program to provide grants for research in the recovering and recycling of critical minerals and rare earth elements found in electronic devices.