An orthodontic appliance such as a bracket is made of a polymeric material with reinforcing fiber structure embedded in the polymeric material. The reinforcing fiber structure includes relatively long filaments that extend about the perimeter of the bracket including the periphery of an archwire slot. In one embodiment, a method for making the bracket includes the steps of placing a tubular fiber preform in a mold assembly in an orientation aligned with a mesial-distal axis of the resultant bracket, and then closing the mold assembly in directions toward a central axis of the preform.