Giordano was born in Hartford, Connecticut. An alumnus of Montgomery Blair High School and Gallaudet University, he began acting in Washington, DC in 1999. He was a member of a small troupe of deaf and hearing actors when he won his first professional role as a member of the Chorus in the Arena Stage production of The Miracle Worker. In 1999, Giordano had obtained his BA in English from Gallaudet University; by September 2001, he played the lead in the critically acclaimed Big River, which originated with Deaf West Theatre, in Los Angeles. Big River was a hit at Deaf West Theatre and made a second run at the Taper Forum. Big River continued its journey, returning to Broadway at the American Airlines Theatre in the summer of 2003, retaining some of its original cast members from 2001 and 2002. Giordano remained with Big River for most of its year-long national tour (June 2004-June 2005) as well as its run in Japan, leaving only to film The Family Stone (2005), in which he played a gay and deaf member of the title family. He also plays the deaf brother of Ashton Kutcher's character in the 2005 film A Lot Like Love and can also be seen in 2008's Untraceable starring Diane Lane. He was recently onstage as Pippin at the Mark Taper Forum, and on film with Russell Crowe in The Next Three Days.