Combine the first 6 ingredients in a large zip-top plastic bag. Add the steak to the bag; seal and marinate in refrigerator 20 minutes, turning occasionally.
Prepare the grill or broiler.
Remove the steak from the bag; discard the marinade. Place the steak on a grill rack or broiler pan coated with cooking spray; cook 5 minutes on each side or until it reaches your desired degree of doneness. Let stand for 5 minutes. Cut the steak diagonally across the grain into thin slices.
In a large bowl, combine the slaw, carrots, onions and cilantro. Toss well.
In a glass measuring cup, whisk together the juice, rice wine vinegar, sugar, ginger, fish sauce, chili garlic sauce and garlic. Pour it over the slaw, and toss to coat.
Divide the steak evenly among the tortillas; spoon about ½ cup slaw onto each tortilla. Fold in half and serve immediately.
