The bony bracket screw has a cross-slot head or a Phillips head and a shank extending from the head, the shank having a smooth upper portion, a threaded lower portion, and a self-tapping or self-drilling tip. The screw has an annual flange defining a stop disposed between the smooth upper shank and the threaded lower shank. The stop may have a larger diameter than the head. The screw has a bracket arm extending from the smooth upper shank at an oblique angle. The free end of the bracket arm has a round retainer, which may be circular or cylindrical and defines a smooth bore adapted for supporting a distractor or other dental appliance. The screw may be made from stainless steel or other noncorrosive, biocompatible material.