Stracci was born in Sicily and immigrated to the US around 1910 with his family. He was reportedly a good friend of Lucky Luciano and they both became members of Giuseppe "Joe the Boss" Masseria's crime family in the 1920s. During Prohibition, Stracci was a bootlegger and extortionist. When Luciano became boss of the crime family he was placed in the crew of Michael "Trigger Mike" Coppola. He soon gained a foothold in the Teamsters union representing the Luciano family.
In the mid-1930s, Stracci and Valachi, along with Frank Livorsi and brother in-law, Joseph Rao, combined their efforts in a numbers racket and he also became a loanshark and had links to the Democratic party and Tammany Hall.
He remained active until the 1970s when he died of natural causes in New York.