Current rating for 12v plug on 300W in-car inverter
Power at the input is the same as power at the output minus inefficiencies or losses.
In your case your inverter will take 300/12 Amps or about 30 Amps allowing for losses.
The cigar lighter  is totally inadequate for this the inverter should be hardwired straight to the battery with a suitable fuse in the wiring near to the battery.