Fill a pan 1/2-inch deep with oil and place over medium heat until hot.

In a large bowl, stir together the shredded chicken, softened cream cheese, sour cream, drained green chiles, cumin, garlic powder, salt, and Monterey Jack cheese until well combined.

Spread a few tablespoons of the chicken mixture in the center of a corn tortilla and roll it up tightly.

Using tongs, carefully set the rolled tortilla seam side down in the hot oil to prevent it from unrolling.

Cook until golden brown and crispy on both sides, then remove to a paper towel-lined plate to drain excess oil.