Preheat oven to 350 F. Grease and flour a 9-inch bundt cake pan. Set aside. In a large bowl, whisk together flour, sugar, cocoa powder, salt, baking powder and baking soda.
Whisk in eggs, root beer, vegetable oil and vanilla extract. Whisk until smooth. Pour batter into the prepared bundt cake pan. Bake for 45-50 minutes. Let cool for 10 minutes in the pan, turn over onto a plate and let cool completely.
For the root beer glaze, whisk together powdered sugar, root beer and vanilla extract until smooth. Drizzle glaze evenly over the cooled cake.
