In a medium bowl, whisk together peanut butter, soy sauce, brown sugar, rice wine vinegar, minced garlic, minced ginger, and sriracha sauce. Adjust texture with water as needed.

In a large mixing bowl, combine cooked chicken, coleslaw mix, and grated carrot. Drizzle half of the peanut sauce over the mixture, toss gently, and let marinate for 5 minutes.

Warm tortillas in the microwave for 30 seconds or on a skillet over low heat for 1 minute per side.

Lay one tortilla flat, scoop filling into the center, fold sides inward, and roll tightly from the bottom up.

Slice wraps in half, drizzle with more peanut sauce if desired, and serve immediately.