Norton worked as a senior attorney at the Mountain States Legal Foundation from 1979-83, and she was a National Fellow at the Hoover Institution during 1983-1984, before taking a position at the U.S. Department of Agriculture as an assistant to Deputy Secretary Richard Edmund Lyng. From 1985 to 1990, she served as Associate Solicitor for the U.S. Department of the Interior, in which capacity she managed attorneys employed by the National Park Service and the U.S. Fish and Wildlife Service.

After leaving the Colorado Attorney General's Office, Norton was a senior counsel at Brownstein, Hyatt & Farber, a Denver-based law firm. And After leaving Washington, she joined Royal Dutch Shell as a general counsel in its exploration and production business. As of 2017, Norton worked for Norton Regulatory Strategies, an Aurora-based consulting firm that deals with environmental regulations. In 2012, she also was a senior adviser for Clean Range Ventures, an energy venture capital firm. She serves as a board member for the Federalist Society, the Reagan Alumni Association, and the Renewable and Sustainable Energy Institute at the University of Colorado.