Born in Reykjavík, Steinunn Birna Ragnarsdóttir studied piano at the Reykjavík College of Music, where she received her soloist’s degree. Her teacher there was Árni Kristjánsson. She received her master’s degree from Boston’s New England Conservatory of Music in 1987 under the tutelage of Leonard Shure. Before returning to Iceland, she lived and worked in Spain, where she appeared as a soloist and performed with numerous chamber ensembles. Steinunn has received various awards for her performances and has appeared in concert in Latvia, Switzerland, Germany, England, France, the Faeroe Islands, the United States, and Lithuania.

A vigorous performer of solo and chamber music, Ragnarsdóttir is an active participant in the cultural life of her native Reykjavík and has performed in many concerts. She has participated in many international Music Festivals and in June 2008 she performed as a soloist with the Virtuosi di Praga Orhestra in the Rudolphinum hall in Prague. Her solo performances with the Iceland Symphony Orchestra include the Grieg Piano Concerto and Icelandic composer Jórunn Viðar’s "Slátta", both of which have been issued on compact disc. She has made numerous other recordings, including a duo album that earned her and cellist Bryndís Halla Gylfadóttir the 1998 Icelandic Music Award for the year’s best classical CD. Their most recent CV since 2008 is called "Myndir á þili".

She is the founder of the Reykholt Chamber Music Festival and was the Artistic Director since 1997 until in August 2010 when she took on the position as the Artistic Director of Harpa Concert Hall and Conference Center in Iceland.