Givens worked for many animation studios during his career, including Disney, Warner Bros. Cartoons, Hanna-Barbera and DePatie-Freleng Enterprises. He began his career during the 1930s and continued until the early 2000s. During his career, Givens created the first design for Bugs Bunny. He worked a lot with director Chuck Jones, working under Jones both at Warner Bros. and Jones' own production company.