In 1994, Norton led the nonpartisan blanket primary for the District F seat on the Shreveport City Council. However, she lost the runoff to fellow Democrat, James Edward Green, who polled 3,762 votes to Norton's 3,615. She fell short again in a three-candidate primary field for the city council in 1998. The post went instead to another Democrat, Joe Shyne, who unseated the incumbent James Green. In 2003, Norton ran for the District 3 state House seat but was defeated by 251 votes by her fellow Democrat, Ernest Baylor, Jr., who polled 3,788 votes to her 3,537,. Four years later, Norton rebounded to claim the seat when Baylor was not a candidate. With 3,901 votes, she defeated her fellow Democrat, Lindora Lee Baker, who received 2,648 votes. Another Democrat, Spencer Stephens, held the remaining 403 votes. In 2011, with 3,078 votes, Representative Norton was forced into a runoff election with Lynn Dale Cawthorne, a Democrat who polled 1,850 votes. In third place was her predecessor, Ernest Baylor, Jr., with 1,548 votes. Republican and subsequently Independent Anna Marie Arpino held the remaining 408 ballots. To score her second term, Norton then defeated Cawthorne in the second round of balloting, 3,240 votes to 2,533. Representative Norton is a member of the Legislative Black Caucus, the Women's Caucus, and the Democratic Caucus. She serves on these committees: Administration of Criminal Justice, Municipal, Parochial and Cultural Affairs, Transportation, Highways, and Public Works, and House Committee on Enrollment. Norton's legislative ratings have ranged from 38 to 67 from the Louisiana Association of Business and Industry. In 2012. the National Federation of Independent Business rated Norton 40 percent. In 2013 and 2014, the conservativeLouisiana Family Forum scored her 67 and 20 percent, respectively. In 2009 and 2013, she was rated 67 and 50 percent, respectively, by Louisiana Right to Life. She was rated 100 percent in both 2013 and 2014 by the Louisiana Association of Educators. In 2014, Norton did not vote on the requirement that abortion providers have hospital admitting privileges near their clinics; only five House members opposed the measure. That same year, she voted to extend the time for implementation of the Common Core State Standards Initiative. She voted to forbid the transportation of dogs in open truck beds on interstate highways. She did not vote on the repeal of state anti-sodomy laws; the measure failed in the House, 27-67. In 2013, Norton voted to reduce penalties for the possession of marijuana. She did not vote on permanent concealed carry gun permits but in 2014 opposed the use of such permits in restaurants that serve alcohol. She opposed keeping information on concealed carry permits confidential and out of the public record. She voted to increase judicial pay and to end the mandatory retirement age for judges. She co-sponsored an "equal pay" plan for state employees. In 2012, she co-sponsored legislation to provide for parole eligibility for non-violent inmates. She did not vote on the prohibition of the use of telephones while driving but opposed making the holding of hand-held devices while driving illegal. She supported state tax incentives to recruit a National Basketball Association team to Louisiana but opposed state income tax deductions for taxpayers donating to scholarship funds. She opposed reducing the number of hours that polling locations remain open; Louisiana has traditionally had 14-hour polling days. In 2011, Norton voted for a permanent tax on cigarettes. That year she also supported parole eligibility for elderly inmates and a failed bill which proposed to halt bullyingin public schools. She opposed the requirement for drug testing of welfare recipients. She voted against the establishment of a commission to develop plan to abolish the state income tax. She supported the redistricting bill for the Louisiana State Senate but opposed the plan for the congressional delegation. In 2010, Norton opposed the carrying of handguns into churches; supporters said the measure would enhance security. In May 2016, Norton acquired national attention when she announced her opposition to a bill which would require that the Declaration of Independence be taught in Louisiana public schools. She declared the Declaration "racist" because it did not apply to slaves. "For the Declaration of Independence, only Caucasians free. And for you to bring a bill to request that our children will recite the Declaration, I think it's a little bit unfair." In 2017, Norton introduced a bill to ban corporal punishment in all Louisiana public schools, but the measure was defeated 61-34. Norton claims other effective measures of discipline can be formulated. She picked up the support of the Republican chairman of the House Education Committee, Nancy Landry of Lafayette, who took the position that only parents should be able to use physical restraint to discipline children. More than half of the Louisiana school districts, thirty-eight of sixty-nine, permit corporal punishment.
