Start with gymnastics. A good gym can give you a leg up on the competition by teaching you basic tumbling and helping you build your strength and agility. Add in some ballet or other dance training, get some stage experience, and take as many specialty classes, like silk rope or trapeze, as you can find in your area.
Attend circus school or camp. There are circus schools in San Francisco, Philadelphia, Florida, Seattle and Evanston, Illinois. Florida State University offers a performing circus for students enrolled at the university, and Dell'Art School of Physical Theatre in Blue Lake, California, offers a Master of Fine Arts in Ensemble-Based Physical Theatre. Most programs offer classes for both children and adults. There are also many programs around the world where you can train as well. Of course, once you are in a circus, they will also send you to their own training program.
Research circuses. There are circuses all over the world and most of them hire acrobats. Do your research, find out what they require and decide which you will apply to.
Prepare a demo tape. Put together a routine that shows off your skills and have it professionally videotaped. Make several copies to send out to circuses.
Apply to the circus. Following each circus's guidelines, apply to join the circus.
Keep working on your skills. A circus acrobat needs to be strong and flexible, which means lots of hard work practicing and maintaining your skills.