I'm not sure this is so, despite a few anecdotal reports. The studies I've seen on circuit training improving cardiovascular fitness show a statistically significant improvement, but not what I would call a dramatic improvement particularly for what a runner would want. I think however that it might help me carry grocery bags into the house from the car quicker and perhaps that might be a good circuit workout in and of itself. More seriously, I think that circuit training would give you the worst of both worlds, rather than the best. You would neither reap the full benefits of strength training nor have anywhere near your best cardiovascular workout.
Cardiovascular workouts are now quite refined and readily measured.
If you use one while performing a circuit workout or while doing strength training, you'll see that you must be performing your exercises fairly quickly and moving from one to the next quite fast without adequate or appropriate intervals between sets to allow for recovery to perform the next set. You also might find that calisthenics, skipping rope, or jogging will be needed to get your heart rate up to the aerobic training zone. This will certainly defeat the purpose of a good strength workout. Why not just do your strength training for the purpose of improving your overall fitness and leave your cardiovascular fitness to your running and cross training workouts. You then are working for specific goals with each specific workout.