In a medium bowl, combine the chopped rhubarb, flour, sugar, baking powder, baking soda, salt, and cinnamon. Mix well to coat the rhubarb with the dry ingredients.
In another bowl, whisk together the egg, milk, and vanilla extract until well combined.
Pour the wet ingredients into the dry ingredients and stir until just combined. Be careful not to overmix; a few lumps are okay.
In a large skillet, heat about 1 inch of vegetable oil over medium heat until hot (around 350°F).
Using a spoon or a small ice cream scoop, carefully drop spoonfuls of the batter into the hot oil. Fry in batches, making sure not to overcrowd the pan. Cook for about 2-3 minutes on each side or until golden brown.
Remove the fritters from the oil and place them on a paper towel-lined plate to drain excess oil.
For the glaze, whisk together the powdered sugar, milk, and vanilla extract in a small bowl until smooth. Adjust the consistency with more milk or powdered sugar as needed.
Drizzle the glaze over the warm fritters before serving.