Anthony was born in New York City in 1943. Her father, the Creative Vice President of Young & Rubicam advertising agency and a cartoonist contributor to The New Yorker, and mother, a singer, raised her and her identical twin sister in Connecticut. After losing their mother to Myasthenia gravis, Anthony and her sister attended boarding school in Massachusetts. Later, she attended Stephens College, Missouri and the Rhode Island School of Design. Anthony graduated in 1966, earning a bachelor's degree in art.