The son of a piano teacher and a book editor for the National Geographic Society, Robinson graduated from the Berklee College of Music in 1981.
The next year, he joined the college's staff, becoming its youngest faculty member.
Robinson has appeared on more than 200 LP and CD releases, including eleven under his leadership, with musicians Lionel Hampton, Anthony Braxton, John Scofield, Joe Lovano, Ella Fitzgerald, Paquito D'Rivera, Sting, Maria Schneider, Elton John, Buck Clayton, and the New York City Opera. Two of these recordings won a Grammy Award. He has received four fellowships from the National Endowment for the Arts.
In 2000, the U.S. State Department named him a jazz ambassador for the year 2001, funding a tour of West Africa in which he played the early works of Louis Armstrong. Material from these appearances was released on the album Jazz Ambassador: Scott Robinson Plays the Compositions of Louis Armstrong by Arbors Records.
Throughout his career, Robinson has worked to keep unusual and obscure instruments in the public view. For example, he has recorded an album featuring the C-melody saxophone and performs with the ophicleide. He also owns and records with a vintage contrabass saxophone so rare that fewer than twenty in playable condition are known to exist.
Since 2009, he has operated his record label, ScienSonic Laboratories.