Finn first appeared in a recurring role, as Julian, on Unfabulous from 2004 until 2007. He has subsequently had many guest starring roles since then, appearing on Lincoln Heights (2009), 90210 (2009), How I Met Your Mother (2009–10), Cold Case (2010), and The Mentalist (2014). Finn has had lead roles in several films directed by his brother, Nika Agiashvili, including The Harsh Life of Veronica Lambert (2009), A Green Story (2012) and Tbilisi, I Love You (2014).
