Born in Hillerød and raised in Birkerød, Sørensen aspired to an acting career after watching the West End production of the musical Chicago while at school.

[4] Sørensen decided in her early teens not to follow her parents' footsteps in pursuing a career in medicine after work experience with her mother at a geriatrics ward.

"[5] While on a school trip to London at the age of 19, she watched the West End production of the musical Chicago which motivated her to become an actress.

[7][8] She continued her studies at the Danish National School of Performing Arts, during which time Sørensen made her acting debut in 2005 as a receptionist on the television series The Eagle.

[15][16] In 2010, she made her breakthrough by playing the idealistic journalist, Katrine Fønsmark, in the DR fictional political drama Borgen which charted the rise of Denmark's first female prime minister.

[19] Sørensen received critical acclaim for playing a strong female protagonist on the show, and international recognition especially in the United Kingdom.

[30] In 2015, Sørensen appeared in the "Hardhome" episode of the HBO fantasy drama series Game of Thrones playing Karsi, a wildling chieftain.

[31] In the same year, she starred with Anna Kendrick in the musical comedy sequel Pitch Perfect 2 as Kommissar, the leader of a rival German a cappella group.