Heat oil in a wok or a deep, wide bottomed pot to 360°F.
While you wait for the oil to get hot, combine the arrowroot flour, coconut flour, coconut sugar and baking soda to a bowl and mix well. Then, add the eggs and coconut milk and mix well.
When the oil is hot, use a small cookie scoop and drop the dough into the oil.
When one side of the donut becomes golden, flip it over and cook the other side for about 3 minutes, or until golden. Fry 3-4 donuts at a time.
Place the fried donuts onto a paper-towel-lined plate.