Haukur played one year of high school basketball in the United States at Montverde Academy under Kevin Sutton.

[1] Haukur came up through the junior ranks of Fjölnir[2] and was first brought up to the senior team during the 2006-2007 Úrvalsdeild karla season when he was an unused substitute in seven games.

[9] In the playoffs they knocked out second seed Stjarnan in the first round[10] before bowing out to the eventual champions KR in the semi-finals.

[12] He spent the 2016–2017 season with Rouen Métropole Basket in the LNB Pro B where he averaged 12.3 points, 4.7 rebounds and 4 assists per game.

[14] On 5 February 2019, he helped Nanterre to the Round of 16 in the 2018–19 Basketball Champions League after scoring 12 points in a 74–62 victory against Hapoel Holon.

[24] He spent most of the first half of the season recovering from an ankle surgery but returned to the court on 3 December 2021 in a victory against Vestri.