Everyone makes valid suggestions but the bottom line is the fan is there already and the electricity has to be adapted to suit it. I'm not sure what the fan is used for and what electical source is going to be used to charge the battery but I agree there are far more efficient ways to move air around.
You are going to need about 15.5W to run the fan and a little more to get it started so a design target would be say 20W. The efficiency of the inverter will be quite low, I estimate 60% and the waveform will not be ideal so add about another 5W to the load calculation. That means the input power from 12V is about 38W. Round it up to 40W to add a safety margin, that means you will draw 3.16 Amps from the battery.
Before going further, do you have a battery capable of sustaining that load? To run if for more than a few hours you would need a small car battery at least.
Brian.