Yes, it is possible to rechagre your car battery at home. And it is not a very difficult task as well.
Put the car battery off frwom the car.
Be careful while to connect battery terminals to the home ups or home invertor.
Red wire of UPS is attached to positive (+ve) terminal of battery and black wire to -ve terminal. Charge you battery fully and again place the battery back to your car.
Click here to watch a small vidoe to understand the whole process of charging the battery with home invertor.