Hi,

No, it can't be charged using a USB cable, as it powers on by inserting either four AA-size alkaline batteries or four AA-size rechargeable nickel-metal hydride (Ni-MH) batteries. Before you use the rechargeable nickel-metal hydride batteries, be sure to fully charge the batteries with the specified battery charger. If you go to the Sony product support website and open the online help guide, under preparation- inserting batteries.
You can also use the external flash battery adapter FA-EBA1 that can be used to provide recycle times as fast as 0.6 seconds.

Sony Europe.

Use normal AA batteries or rechargeable AA batteries.
Cannot be charged with USB c.