Yes, you can take a banjo on an airplane. It is recommended, however, that you take it with you on carry-on, rather than stowing it with the larger luggage, unless you have it very well protected, as it is likely to get quite knocked around otherwise. Most smaller models (especially mini sized ones) are fine for carry-on, but even then, it would be best to take it in a sufficiently padded gig bag or, even better, a hard case. Luckily the U.S. and some other countries have legislation against charging passengers extra for taking instruments on carry-on.