Cody was born Espera Oscar de Corti on April 3, 1904, in Kaplan in Vermilion Parish, in southwestern Louisiana, a second son of Francesca Salpietra from Sicily and her husband, Antonio de Corti from southern Italy. He had two brothers, Joseph and Frank, and a sister, Victoria. His parents had a local grocery store in Gueydan, Louisiana, where he grew up. His father left the family and moved to Texas, where he took the name Tony Corti. His mother married Alton Abshire and had five more children with him.