Whisk together cake flour, sugar, cocoa powder, baking powder, baking soda, and salt in a large bowl. Make a well in the middle of the dry ingredients
Whisk water, vegetable oil, vinegar, and vanilla extract in a separate bowl until thoroughly combined; pour the wet ingredients into the well in flour mixture.
Stir until batter is smooth. Pour into prepared cake pan.
Bake in preheated oven until cake springs back when lightly touched and a toothpick inserted into the center comes out clean, about 45 minutes.
Cool in pan on wire rack for 15 minutes before removing cake to finish cooling on rack.