I found this elsewhere

"The easiest way to acquire more Virginia creeper vines is to take stem cuttings and root them. Cut off a 4 or 5 inch length of new growth or pinch off a tender sucker that has sprouted from the stem of the vine. Strip the leaves off near the cut end and dip it into rooting hormone. This powder is readily available at garden centers. Then stick the cutting in a shallow dish or box of moistened sand, perlite or soilless potting mix. In a week or 10 days thin fibrous roots should begin to develop. When they are an inch or so long, the cuttings can be planted in pots, or outdoors."

I've never taken cuttings of virginia creeper but a more certain method than that shown above( but slower) is to layer a stem.

Just pin down a stem,cover it with a bit of soil/compost cover it with a stone and keep moist. It will root into the soil and you can chop it off and you have a nice rooted new plant.