Skorstad, who competed for the Rustad IL , ran internationally for the first time in November 1994 in the Continental Cup in Beitostølen and achieved 40th place over 10 km classic. He had his debut in the World Cup in March 1996 in Oslo , which he finished in 16th place with the relay. He completed his first of a total of 22 individual World Cup races in March 1998 in Oslo, which he finished classically in 51st place over 50 km. In the 2000/01 season he got his first World Cup points with 16th place over 15 km classic in Beitostølen and 11th place over 50 km classic in Oslo. In addition, he won his only classic race in the Continental Cup in Mäntyharju over 30 km. In the following season he came in five World Cup appearances twice in the top ten. He achieved his best individual placement in the World Cup with fifth place in the Birkebeinerrennet and his best overall result at the end of the season with 52nd place in the overall World Cup. In addition, he won the Tartu Maraton that season and thus achieved 11th place in the overall ranking of the Marathon Cup . His last World Cup race was the Wasalauf in March 2006 , which he finished in 50th place.
At Norwegian championships , Skorstad was third over 10 km in 1998 and second over 30 km in 2002.