Sorry, but no way realistically. I mean you could do it in theory... but we're talking about a 1000 watt solar system and a massive battery bank and inverter.
Problem is you are taking a 12 volt DC power source and trying to run a 120 volt AC appliance off of it without doing the conversion or accounting for your batteries. Your air conditioner doesn't run on 12 volts. A 20 amp load at 120 volts is 2,400 watts of continuous power. You'll also need a big inverter, which will increase your losses.
Even with 320 watts of (DC) solar panels, you aren't anywhere close to supporting the demands of a 2400 watt AC current appliance for more than a few minutes.
Another way to think about it is this...
People often purchase a generator that puts out more than 3000 watts of 120 Volt power to run their air conditioner. Your solar panel puts out 300 watts of 12 volt DC power under ideal conditions - a fraction of what you would actually need.
Here's a video -
These guys had a 700 amp hour battery bank (my camper came with a 75 amp hour battery, not sure about yours..) I would just add that the video above has often been called out for being overly optimistic. These guys have a massive system and they were able to run their AC for about an hour before they were risking their very expensive / large battery bank.