Add enough oil to a heavy bottom straight-sided pan to come 2 inches up the sides. Heat over medium heat to 350 degrees F on a deep-fry thermometer.
Meanwhile, mix together the chicken, Cheddar, 1/2 cup salsa and the cumin in a medium bowl. Spoon about a 1/4 cup of the mixture into the center of each tortilla. Roll the tortillas tightly around the filling and secure with a toothpick.
Working in batches of 2 or 3 at a time, place the taquitos in the hot oil and fry, flipping as needed to brown evenly, until crispy and golden brown, about 3 minutes. Using tongs, remove the taquitos to a paper-towel lined plate to drain. Continue with the remaining taquitos. Serve alongside salsa and sour cream for dipping, if desired.