Preheat an oven to 350 degrees F (175 degrees C). Grease a 9x13-inch baking pan.
Heat the butter, sugar, cinnamon, and vanilla in a saucepan over medium heat until the sugar dissolves, about 5 minutes. Remove from heat; set aside. Divide the crescent roll dough into 16 triangles. Roll 1 slice of apple with the dough and arrange on the prepared pan. Pour the butter mixture over the wrapped apples, then pour the citrus-flavored soda on top.
Bake in the preheated oven until golden brown, 40 to 45 minutes.
