Preheat oven to 350°F (175°C). Grease and line an 8-inch cake pan.
Sift together flour, cocoa powder, baking powder, and salt in a bowl.
In another bowl, whisk soy milk, vinegar, sugar, oil, and vanilla extract.
Combine wet and dry ingredients until smooth.
Pour batter into the pan and bake for 30-35 minutes or until a toothpick comes out clean.
Cool for 10 minutes in the pan, then transfer to a wire rack to cool completely.