Remove the door from the cabinet using an electric drill or a screwdriver to pull out the screws. Look at the affected screw holes to estimate their size. Purchase a short section of wooden doweling approximately the same size or slightly larger than the hole.
Measure the length of the hinge screw. Mark this measurement on your drill bit with a piece of masking tape. The drill bit needs to be the same width as the doweling. Drill out the screw holes to the marked depth. Blow into the holes to remove any sawdust.
Cut sections of doweling the same length as the hinge screws, using a fine-toothed saw. Dip the doweling into carpenter’s glue, and tap into the drilled-out holes. Use a rag to clean off any excess glue. Let the glue dry according to the manufacturer's recommendation, or overnight.
Position the hinge over the filled holes, and mark with a pencil where the screws should go. Drill pilot holes into the wood of the dowels. Situate the hinge, and screw into place.