Prepare a pot or planting container by filling it with a 50/50 mixture of perlite and peat moss. Then poke a hole in the peat moss mixture for the cutting using a pencil.
Remove the leaves from the bottom two-thirds of the cutting, leaving at least four leaves on the cutting.
Strip away the thin outer layer or bark of the cutting on one side starting at about 1/2-inch above the bottom and continuing all the way down so that the inner layers are expose on one side. This will help the roots form.
Dip the end of the cutting into root growth hormone, making sure to cover the area that you stripped away.
Poke the cutting into the pot, with the cut end down, so that it stands straight up.
Water the cutting thoroughly.
Create a tent over the pot with either clear plastic wrap or a clear plastic bag. Secure with a rubber band so that air does not escape.
Place the pot in a location that maintains a steady warm temperature, ideally around 70 degrees, and receives plenty of filtered sunlight.
Wait about two months, checking the plant occasionally and adding water if needed to keep it moist. Gently push back the soil at the end of two months to check for root growth, being careful not to damage the new roots.
Remove the plastic wrap once roots are identified and transplant the new rhododendron plant as desired.