Is it possible for you to have braces if you have one false tooth?

Usually: Depending on what you describe as a false tooth, orthodontists can fabricate a plan which will take into account missing or false teeth.

Yes, but...: If false tooth is part of a bridge, it may have to be sectioned, the teeth moved, and the bridge remade. If implant/crown, may have to be replaced when the rest of your dentition has been optimized. Talk to a qualified orthodontic specialist. We deal with situations like this every day.