Turn off the power to the receptacle at the home's circuit breaker panel.
Remove the screw holding the receptacle's cover plate. Remove the plate. Remove the screws at the top and bottom of the receptacle. Pull the receptacle out of the outlet box. Loosen the screws on the side of the receptacle and take off the wires connected to the receptacle. Loosen the screws holding the outlet box in the wall and pull the box out of the wall.
Place your light fixture box against the wall, above the receptacle at the location you've chosen for the light. Trace the light fixture box's perimeter onto the wall with a pencil. Cut out the traced area with a keyhole saw.
Slide a length of 12-2 electrical cable into the light fixture hole, fishing it down to the opening in the wall for the receptacle. Pull a couple feet of cable out of the receptacle hole. Remove 1/2 inch of insulation from the wires at the ends of the cable at the receptacle opening.
Cut a 6-inch piece of electrical cable. Remove 1/2 inch of insulation from the wires at both ends of the cable. Attach the wires from one end of this cable to the screws of the receptacle, matching the black wire to the brass screw and the white wire to the silver screw. Slide the receptacle box over the cable attached to the receptacle, using the opening in the top of the outlet box.
Match the bare ends of the cable attached to the receptacle to the end of the new cable that runs to the light fixture opening. Place wire nuts over each of the paired wires and twist until they're tight. Wrap electrical tape around the wire nuts.
Push the receptacle into the receptacle box, taking up the slack in the cable from the top. Attach the receptacle to the outlet box.
Slide the other end of the new cable through the opening in the bottom of the light fixture box. Place the fixture box into the opening and secure it to the wall with the screw tabs of the light fixture box.
Trim the new cable so there are about 6 inches of cable extending out of the box. Remove 1/2 inch of insulation from the ends of the cable's wires. Attach the wire ends to the new light fixture, following the light's instructions. Place the light in position on the light fixture box and attach according to instructions. Turn the power back onto the circuit when the light is installed.