Norton's first assignment out of West Point was to 12th Infantry Regiment, 4th Infantry Division as a company commander. He then returned to Infantry School in the fall of 1942 to attend the Battalion Commander and Staff Officers Course and the Parachute Course. Following his completion of the course, he reported to the 82nd Airborne Division in North Africa. He was soon promoted to executive officer of the 2d Battalion, 505th Parachute Infantry Regiment. Two months later, he was again promoted, to S-3 (operations officer) of the Regiment. He made his first of four combat jumps as an executive officer, participating in the Invasion of Sicily. After returning to North Africa, he made a second combat jump into Salerno, Italy, blocking German forces who were trying to attack US amphibious forces. His third jump was in support of the Invasion of Normandy on D-Day, 6 June 1944 when he led his men in the dark over St. Mere-Eglise, France. In July of that year, he assumed command of the 3d Battalion; he was promoted the next month to G3 of the 82d Airborne Division. Norton made his fourth combat jump in September, in the Netherlands to take control of the bridges from the Dutch border to Arnhem as part of Operation Market Garden.