Place chickpeas in a food processor; pulse 3 times or until chopped. Combine chickpeas, apricots, and next 7 ingredients (through turkey). Divide mixture into 6 equal portions, shaping each into a 1/2-inch-thick patty.
Place patties on a grill rack coated with cooking spray; grill 6 minutes on each side or until a meat thermometer registers 165°. Remove from grill; let stand 5 minutes.
Place buns, cut sides down, on grill rack; grill 1 minute or until toasted. Place 1 patty on bottom half of each bun; top each serving with 1 tablespoon tzatziki sauce and top half of bun.