Spector has appeared in the TV series Allegiance (2015), The Mist (2017), Homeland (2018), and Pearson (2019), as well as the films The Drop (2014), Christine (2016), A Vigilante (2018), and Boston Strangler (2023).

[7] After graduating from Reed College, in Portland, Oregon, he enrolled in the acting school of the American Conservatory Theater, in San Francisco.

[7] In 2010, Spector made his Broadway debut as Rodolpho in Gregory Mosher's revival of Arthur Miller's play A View from the Bridge.

[12][13] In September 2015, Spector married actress Rebecca Hall, whom he had first met the year before, during their work together in the Broadway play Machinal.

[15] In 2024, along with 30 other artists, Spector participated in publicly reading the dossier of South Africa's genocide case against Israel, which was brought before the International Court of Justice.