Orci was born in Mexico City on July 20, 1973, to a Mexican father and a Cuban mother. His mother immigrated to the United States with her parents after Fidel Castro came to power. Orci grew up in Mexico, and moved with his family to the United States at the age of 10. He was raised in Texas, Los Angeles and Canada. He is the older brother of screenwriter-producer J. R. Orci.