Preheat oven to 250 degrees F (120 degrees C). Grease a 9x13-inch baking dish.
Bring sugar, butter, cocoa powder, and corn syrup to a gentle boil in a saucepan; cook until thickened, 1 to 2 minutes. Stir in vanilla extract. Pour popcorn into a large bowl, add cocoa mixture and stir until popcorn is well coated. Spread evenly in prepared baking dish.
Bake in the preheated oven, stirring occasionally, until mixture is set, about 30 minutes.
Remove from oven and cool to room temperature; break into clumps.