Choose a mature, healthy rosemary plant to take your cutting from in the spring when the plant has resumed active growth. This cutting will grow into a clone of the host plant, so pick one that you like.
Snip a 2- to 3-inch stem tip from this year's new growth with a clean, sharp knife or scissors. Clip the leaves from the lower two-thirds of the stem. Leave at least five or six leaves at the top.
Combine equal parts peat moss and perlite. Fill a 2-inch pot with the rooting medium to within 1/2 inch of the rim. Set the pot in a container of warm water until the surface of the medium feels moist. Take the pot out of the water and allow it to drain freely for about an hour.
Moisten the lower 1/4 inch of the rosemary cutting with water and dip it in powdered rooting hormone, if you wish. Make a 1/2-inch-deep depression in the center of the rooting medium. Plant the rosemary cutting and firm the medium around the stem.
Cover the pot with a plastic bag to create a miniature greenhouse. Secure it with a rubber band around the pot.
Set the rosemary cutting in a warm, brightly lit spot out of direct sunlight. A warm windowsill or the top of your refrigerator are good locations. Your cutting will root in 14 to 21 days.
Check the rooting medium every day to make sure that it never dries out. Keep it evenly moist but not wet or soggy.
Remove the plastic bag when you see new growth emerge from the rooted cutting. Step it up to a bigger pot, or plant it outdoors.