Place all the ingredients, except the salt and pepper, in the bowl of a food processor. Blend until the mixture is smooth.
Add the shredded chicken to the aioli and mix well. Preheat a heavy-bottomed skillet over medium heat. Using tongs, add the tortillas, 1 at a time, and cook until warm, about 30 seconds each side.
Place the warm tortillas on a work surface and spread with the chicken mixture, leaving a 1/2-inch border.
Sprinkle the arugula over the chicken mixture. Carefully roll up the tortillas, jelly-roll fashion.
Cut each rolled sandwich in half, diagonally, and transfer to a serving platter.