In 1977, at the age of 10, Scarpelli made his Broadway debut, appearing in the play Golda with Anne Bancroft. He returned to the stage in 1979 with the role of Richard, Duke of York in the Broadway revival of Richard III starring Al Pacino.
Scarpelli's role as Alex Handris (1980–83) on the long-running television situation comedy One Day at a Time is his most prominent. He left that sitcom to appear in the NBC sitcom Jennifer Slept Here. Other television appearances include 3-2-1 Contact, Steven Spielberg's Amazing Stories, MacGyver and The Love Boat. He was also a co-host in summer 1983 of the NBC game show/human interest show Fantasy.
He released a self-titled pop album in 1983, which included the single "Get a Love On".
Born in Staten Island, New York City, New York, he is the son of long time Archie Comics Artist Henry Scarpelli. (Glenn would feature in issue #330 of Archie, dated July 1984). He attended a private Catholic school, St. Joseph Hill Academy, from kindergarten to 8th grade.
He has remained close friends with One Day at a Time co-stars Mackenzie Phillips and Bonnie Franklin until her death in 2013.