Rocca was born in Washington, D.C.; his mother immigrated there from Bogotá, Colombia in 1956 at age 28, and his father was a third generation Italian-American from Leominster, Massachusetts. He attended Georgetown Preparatory School, a Jesuit boys' school in North Bethesda, Maryland. He graduated from Harvard University in 1991 with a bachelor of arts degree in literature. He served as President of Harvard's Hasty Pudding Theatricals, performing in four of the company's notorious burlesques and co-authoring one (Suede Expectations).