Warm oil in large skillet over medium heat. Add garlic, ginger and scallions and stir until fragrant, about 1 minute. Add chicken, hoisin sauce, vinegar and cashews and cook, stirring, until heated through, 2 to 3 minutes.
Warm tortillas in microwave just to soften. Lay tortillas on a work surface. Divide lettuce among tortillas. Spoon chicken mixture into middle of each tortilla, sprinkle with carrots, wrap and serve.