A bioabsorbable interference screw having a tapered profile which extends along substantially the entire length of the screw. The tapered profile makes the screw easy to insert while providing superior fixation resulting from a progressively increasing diameter. Upon insertion, the screw engages cortical bone at the back end of the bone tunnel and fills all but 5-10 mm. of the tunnel, thereby providing increased fixation strength while also promoting fast healing. The screw includes a head provided with a specially designed drive socket with radially extending slots at its outer end for receiving corresponding protrusions on the shaft of screwdriver. The drive socket optimizes the torque capacity of the screw. To maintain wall thickness, the socket has a taper corresponding to the tapered outer profile of the screw. The taper of the socket also permits easy insertion of the tip and shaft of the driver into the screw.