Superglue can work sometimes on some types of plastic and if the repair is small the superglue might just do the job.
But what I would recommend for gluing plastic back together is the glue for plastics known as plastic cement which I found works better at gluing plastic together.
I've had superglue work okay to glue some plastic but I've found the plastic cement bonds the plastic together much faster and stronger than superglue does.
The best glue to use for gluing plastic together is Loctite Epoxy Plastic Binder which does a great job when gluing plastic together and works on almost all types of plastic when you need to glue it together.