No, a 100 watt solar panel cannot run an air conditioner. Air conditioners require a lot of power to run, and 100 watts is not enough. You need at least 300 watts to run a low-watt air conditioner. However, you could use a 100 watt solar panel to offset some of the power consumption of an air conditioner. For example, if your air conditioner uses 800 watts, you could use a 100 watt solar panel to offset about 12.5% of that power usage.