Victor Halperin's White Zombie was released in 1932 and is often cited as the first zombie film.
Wikipedia - List of Zombie films
White Zombie is considered to be the first feature length zombie film and has been described as the archetype and model of all zombie movies. Not many early horror films followed White Zombie's Haitian origins style. Other horror films from the 1930s borrowed themes from White Zombie, such as people returning from the dead and other elements of zombie mythology. These films include: The Ghost Breakers (1940), King of the Zombies (1941), I Walked with a Zombie (1943), and The Plague of the Zombies (1966). These films all contain elements from White Zombie including the blank-eyed stares, the voodoo drums, and zombies performing manual labor.