Depending on your cabin of travel and EC status, the size may not be a huge issue (most CSDs will be accommodating to items as big as a guitar), but getting through security is a different matter altogether. BA has no say at all whether or not you can bring it through security, so to avoid trouble you may want to pack it well and check it in or confirm with each country the security regulations regarding badminton rackets. Storing a badminton racket on board isn't much of a problem though, as they are very thin and could be squeezed into a coat locker.

Either way, good luck!