Sjálvstýrisflokkurin
Skorheim was leader of Unga Sjálvstýri until 2011. He has been a member of the town council of Klaksvík since 1 January 2009, and deputy mayor, chairman of Culture Affairs, deputy chairman of Finance Committee and member of Technical Committee from 1 January 2009 until 31 December 2012. Since 1 January 2013 he is the mayor of Klaksvík representing Self-Government Party (Sjálvstýrisflokkurin), together with Tjóðveldi and Javnaðarflokkurin.