Arquette was born in New York City, the son of Brenda Olivia "Mardi" (née Nowak), an actress, poet, theater operator, acting teacher, and therapist, and Lewis Arquette, an actor. Arquette's paternal grandfather was comedian Cliff Arquette. Arquette's mother was Jewish (from a family that immigrated from Poland and Russia). His father, whose family's surname was originally "Arcouet", was of part French-Canadian descent. Arquette's father was a convert from Catholicism to Islam, and through him, Richmond is distantly related to explorer Meriwether Lewis. His siblings are actors Rosanna, Patricia, David, and the late Alexis Arquette. He was the brother-in-law of actress Courteney Cox and actor Thomas Jane.