Preheat oven to 350 degrees F (175 degrees C). Grease a 9x13-inch baking dish.
Whisk flour, baking soda, and baking powder in a bowl. Beat butter and brown sugar with an electric mixer in a separate large bowl until smooth, and stir in sour cream, egg, and vanilla extract, mixing well. Stir flour mixture into sour cream mixture just until incorporated; pour batter into prepared baking dish. Spread rhubarb over batter. Mix white sugar with cinnamon in a small bowl and sprinkle the cinnamon sugar over the rhubarb.
Bake in the preheated oven until a toothpick inserted into the center of the cake comes out clean, 35 to 45 minutes.