David Bennett is Annie's biological father.
As Agent Ness of the FBI revealed in the final chapters of the novelisation, David, along with his wife Margaret Bennett, were struggling artists from Iowa who went to New York City in order to study art at Cooper Union. With no known immediate relatives to call for, David left his daughter Annie at the orphanage as his wife contracted influenza, hoping he and Margaret would come back as soon as Annie's mother gets well. Margaret sadly succumbed to her illness on January 13, 1922; David Bennett had also died as well, having contracted the disease from his wife. David was described as "tall and square-jawed, with a mop of unruly red hair."
Later renditions of the musical adaptations would change their backstory somewhat, with David and Margaret having died in a fire - this alternate backstory would be used in the 1982 and 1999 renditions.