Nothing will happened except you will be needing a new charging cable. Most smartphone chargers charges your phones at 5v DC (direct current) and with about 1–2 Amps, and these voltages and currents are not nearly enough to kill anyone, not even a fly, let alone a cat.
Even if the cat bites into the AC side of the charger, most of them are thick plastic and can’t be bitten that easily… The risk of shock is quite low, but it’s there. Just plug the charger high ground or somewhere cat can’t reach it and that should solve the problem.