This is a yes/no question so you would raise your eyebrows for the whole question. New signers would typically sign this question word by word: HAVE YOU EAT/FOOD? But by simply signing HAVE YOU EAT/FOOD, it does not express the fact that we are asking whether something has been completed. Signing it like this makes it a very unclear question that almost looks like you're asking if someone has some food.
In ASL we use the sign FINISH to represent completion. So in this case, we would sign: EAT/FOOD FINISH YOU? We typically place FINISH before or after the verb - so FINISH EAT/FOOD YOU is okay too. You can also use the standard simple statement: YOU FINISH EAT YOU?