Mix pork, green onions, water chestnuts, soy sauce, cornstarch, salt, and ginger in a medium bowl until well combined. Spoon 1/2 teaspoon pork mixture into the center of a wonton skin. Fold wonton skin over filling to form a triangle. Turn the top of the triangle down to meet the fold, then flip over. Moisten one corner with water; pull the opposite corner over the moistened corner to overlap, then press together firmly to seal. Repeat to make remaining wontons.

Heat oil in a wok or large saucepan over medium-high heat to 375 degrees F (190 degrees C). Deep-fry a few wontons at a time until brown and crispy, 2 to 3 minutes. Drain on paper towels and serve warm.