Possibly. Bicycles, like all products, can injure consumers when a defect renders them unreasonably dangerous. Many bicycles are recalled every year because they pose unacceptable hazards to riders. If your bicycle was dangerous and defective, then you could sue the manufacturer for your injuries.
For example, Trek recalled about a million bicycles because a lever on the front wheel caused the bicycle wheel to completely separate. One person was paralyzed and others were injured before the manufacturer pulled the bicycle from the marketplace. Your bicycle accident attorney will need to thoroughly review the circumstances of the crash and possibly look at the bicycle before determining whether you have a case.