A full international between 2007 and 2020, he won 97 caps for the Iceland national team and represented his country at the UEFA Euro 2016, reaching the quarter-finals, and the 2018 FIFA World Cup.

In November 2022 Ragnar was introduced as assistant-manager of Fram Reykjavik and in July 2023 he became a caretaker-manager of the side following the departure of his predecessor Jón Þórir Sveinsson.

He would go on to play 90 minutes in all 26 of the club's league matches, forming a formidable partnership with Mattias Bjärsmyr as the team won Allsvenskan 2007.

IFK Göteborg's sports director, Håkan Mild commented that the club could get a transfer fee around €3 million for the talented defender.

[5] On 23 January 2014, Russian Football Premier League club FC Krasnodar announced they had signed Ragnar on a two-and-a-half-year deal with option for another year.

[9] On 18 January 2018, he signed a deal for a permanent transfer to FC Rostov, the third Russian club of his career, where he joined his Iceland national teammates Sverrir Ingi Ingason and Björn Bergmann Sigurðarson.

[12] On 18 January 2021, Sigurðsson moved to Ukrainian Premier League side Rukh Lviv, signing a contract until the summer of 2021, with an option to prolong the deal for another year.