Capone would have been the right age for WWI. I read that he told people that he was a part of the Lost Battalion, of which only 194 were rescued out of 544 men. Supposedly, this is how he got the maimed face, and his moniker, Scarface. Is there any truth to it?
I was looking into this for you, and it doesn't seem like that's true, though I can still be wrong. I was looking at his Wiki page and there was a lot going on in his life around that time, but they never mention him going to war. The truth about those scars are that he got slashed with a pocket knife when he was a bouncer in a bar.
No, Alphonse "Scarface" Capone never fought in World War I nor served in the US Army. The only documented member of his family to do so was James Vincenzo Capone (aka Richard James Hart) who, somewhat ironically, was a Prohibition agent after the war.