Combine the carbonated water, sugar and root beer concentrate in an extra-large bowl or punch bowl - something that is food-safe and won't break when the dry ice is added. Don't cover with a lid. Gently stir until the sugar is dissolved. Add the dry ice to the mixture in a well-ventilated area. The mixture will start to bubble. Let the mixture sit for 15 minutes to fully carbonate.
Ladle some of the root beer into a glass. Top with desired amount of vanilla ice cream.