A swivel suture anchor for knotless fixation of tissue. The suture anchor includes an anchor tip configured to capture suture, the anchor tip being rotatably received within a fixation device upon advancement of the fixation device over a shaft of the anchor tip. The anchor tip is configured to receive a suture to be anchor in bone without requiring suture knots. The anchor tip can be a conical metal tip which is self-punching and avoids the need for pre-drilling a hole in bone. The anchor tip includes a closed aperture to allow free sliding of a suture strand. The suture is secured in a hole in bone by inserting the anchor tip into bone, and advancing a fenestrated fixation device, such as a cannulated interference screw, over a shaft of the anchor tip.