Preheat the oven to 350° Celsius.
Take the muffin cups and grease them well. You can also take butter and apply it at the inner surface of the cups.
Take butter, sugar and eggs in a large bowl and beat them together to form a cream. Make sure the sugar is well dissolved in the mixture. Add in milk, vanilla and rice and beat them on medium pace.
Now, add baking powder, rice flour, cornstarch and salt to the mixture and stir with spatula. Make sure you do not over mix the ingredients. Fold in cranberries and spoon the mixture into the already prepared muffin cups, evenly distributed.
Place the muffins in the oven and bake for around 20 to 25 minutes. Take them and serve.