Staying less than 6 months
If you are a national of a Nordic country who intends to work in Iceland for less than six months, you need to contact Iceland Revenue and Customs (Skatturinn), regarding the application of a system ID number.
You can find the relevant form RSK 3.30 Application of a system ID number from Iceland Revenue and Customs. A tax card is issued following the allocation of a system ID number. You cannot apply for a system ID number yourself but you do need to request Iceland Revenue and Customs to apply for you. A system ID number does not grant you any rights in Iceland and does not confirm your right to residency in the country.