Þóra had already spent the 2004 season in Norway as Bente Nordby's understudy at Kolbotn, when in January 2007 the opportunity to move to Belgium came up through her career outside football.

[3] In August 2007 she left Anderlecht to join sister Ásthildur in Sweden at Malmö, who needed a goalkeeper due to Caroline Jönsson's anterior cruciate ligament injury.

[7] Þóra was named Damallsvenskan goalkeeper of the year in 2012 and 2013 after keeping 14 "clean sheets" as Malmö recaptured the league title from rivals Tyresö FF.

National team coach Siggi Eyjólfsson selected Þóra in the Iceland squad for UEFA Women's Euro 2013,[10] although she was recovering from a hamstring injury.

[13] Sigurwin came to prominence during the tournament when Ludvig Lindström of Global Happiness Organization (GHO) publicly criticised the players for keeping him in a jar and making jokes about flushing him down the toilet.