Right now, curling wands, curlers without clamps, are becoming more and more popular. They're great because they allow you to better control the size and shape of your curl, without ruining your look with kinks created by those pesky clamps.
If you're not ready to upgrade your curler or simply can't afford to right now, you can definitely use your old styling tool to help you achieve the same look. Just leave the clamp down and very carefully wrap your hair around the closed curler. It's an instant curling wand.
For safety reasons, I recommend buying a heat resistant glove or grabbing an old oven mitt.