Place peeled potatoes in a large pot and cover with cold water. Bring to a boil and cook for 6 to 7 minutes until partially tender but still firm in the center.
Drain the potatoes and allow them to steam dry in a colander for 5 minutes until cool enough to handle.
Using the large holes of a box grater, shred the potatoes into a large mixing bowl.
Squeeze the shredded potatoes in a clean kitchen towel to remove any excess moisture.
Sprinkle the shredded potatoes with gluten-free flour, garlic powder, onion powder, salt, and black pepper. Toss gently until evenly coated.
Form the mixture into small cylinders, approximately 1 inch long and 3/4 inch wide, pressing firmly to ensure they hold their shape.
Heat the vegetable oil in a heavy-bottomed pot or deep fryer to 375°F (190°C).
Fry the tots in small batches for 3 to 4 minutes until golden brown and crispy. Drain on paper towels and serve immediately.