From what I understand all vodkas are gluten free due to the distillation process even if made from a gluten containing grain. The only time you would have problems is if something is added afterwards.
I used to think that vodka made from grain was causing me problems. It was actually the bar coke from the soda gun. Still not worked out which bar it is that has gluten in the syrup for the coke
Smirnoff is corn based if you are worried.