Position the baking rack in the middle of the oven, and preheat to 400F. Line a baking sheet with parchment paper.
In a large bowl, combine the beans, corn, salsa, cheese, cumin, and garlic powder, and stir to evenly distribute the ingredients.
Soften 2-3 tortillas at a time by placing them in between 2 damp paper towels and microwaving for 20 seconds. Alternatively, you can warm them on a heated griddle.
Place the warmed tortillas onto a flat surface and add 2 tablespoons of the filling mixture onto one edge of each tortilla. Roll the tortilla into itself and transfer it to the lined baking sheet.
Use a toothpick to secure each taquito in place. Repeat the process with the remaining tortillas and filling.
Brush or spray the taquitos with oil, and bake for 22-25 minutes until the tops are golden brown and the tortillas are crispy.