Fill a 6-quart heavy pot or Dutch oven two-thirds of the way full with oil. Heat the oil over medium-high heat until a deep-fat thermometer registers 375 degrees F.
Cut the potatoes lengthwise into 1/4-inch-thick sticks. Fry the potatoes in batches, until golden brown, 8 minutes per batch. Transfer the potatoes with a slotted spoon to a paper-towel-lined baking sheet. Sprinkle with celery salt and serve immediately.