A self-aligning swaging punch is provided for adjoining together a pin and a workpiece having a pinhole. The swaging punch comprises a shaft and a tip having an open-ended cavity. The shaft transfers an axial force from a press or hammer to the tip. The tip transfers the axial force from the shaft to a top surface of the workpiece near the pinhole. The tip may be spherical in shape for evenly deforming the workpiece near the upper edge of the pinhole. The open-ended cavity receives the pin therein and allows the pin to extend at least partially into the open-ended cavity while the tip contacts the workpiece. The open-ended cavity also ensures that the swaging punch is aligned with the pinhole and perpendicular to the surface of the workpiece when the pin is inserted into the pinhole such that the workpiece evenly deforms and presses against the pin.