Camargo is a graduate of the Juilliard School, where he was a member of the Drama Division's Group 25 (1992–96). He went on to perform in the 1996 Broadway production of David Hare's Skylight with Michael Gambon (Theater World Award). From there, Camargo went to England to join the inaugural company of Shakespeare's Globe Theatre on the Southbank. He met his Future wife, English Actress Juliet Rylance, there.
Camargo's New York theater work includes the Public Theater's Kit Marlowe, Steve Martin's Underpants at Classic Stage Company, and the title role of Theater For A New Audience's Coriolanus. In 2008, Camargo played opposite Dianne Wiest, John Lithgow and Katie Holmes in Arthur Miller's All My Sons on Broadway. In early 2009, he played the title role in the Theatre for a New Audience's production of Hamlet. He won an Obie and Drama League nomination for his performance. The show ran until April 12, 2009.
Camargo portrayed Orlando in The Bridge Project's presentation of Shakespeare's As You Like It in Brooklyn, New York. In February 2010, he played Ariel in the company's rendition of Shakespeare's The Tempest. Both plays were directed by British Director Sam Mendes. On September 30, 2010, he was cast as Eleazar in The Twilight Saga: Breaking Dawn, Parts 1 and 2.
Camargo wrote and directed Days and Nights, a modern retelling of Anton Chekhov's The Seagull, produced by his wife, Actress Juliet Rylance, together with Barbara Romer, founder of the New Globe Theater. The film was scheduled for a 2014 release. He recently portrayed Mercutio in the 2013 Broadway revival of Romeo and Juliet, directed by David Leveaux and starring Orlando Bloom as Romeo and Condola Rashād as Juliet. He guest starred as Wade Crocker on the third season of Syfy's Haven.
Camargo portrayed the title character of the Theatre for a New Audience off-Broadway production of Pericles, directed by Trevor Nunn, from February to April 2016. In May of that year he guest starred as Dracula on the third season of Showtime's Penny Dreadful.
In March and April 2017, Camargo portrayed a mid-career Robert Evans in Simon McBurney's stage adaptation of The Kid Stays in the Picture, staged in London's Royal Court Theatre.
