No, it is not possible to plug a standard household refrigerator into the cigarette lighter socket (also known as the 12V accessory socket) of a car. Household refrigerators typically require a much higher power supply than what a car's cigarette lighter socket can provide.
A typical car's cigarette lighter socket is designed to supply 12V DC (direct current) power, and its maximum power output is usually limited to around 120 watts. On the other hand, a standard household refrigerator requires 110-120V AC (alternating current) power and consumes much more power than what a car's socket can deliver. Household refrigerators can require anywhere from a few hundred to over a thousand watts of power, depending on their size and efficiency.
Even if you were to use a power inverter to convert the car's 12V DC power to 110-120V AC, the power draw from the refrigerator would likely exceed what the car's electrical system can handle. Running a household refrigerator from a car's power system could drain the car's battery quickly and potentially cause damage to the car's electrical components.
If you need to keep food or beverages cool while traveling, it's best to use a dedicated portable car refrigerator or cooler that is specifically designed to operate on 12V DC power and is suitable for use in vehicles. These portable car refrigerators are designed to be energy-efficient and won't put excessive strain on your car's electrical system.
Always follow the manufacturer's instructions and recommendations for any electrical appliances used in your car to ensure safe and proper operation.