Can a portable power station run a refrigerator?

Possibly, depending on the fridge and the portable power station.

For example, this standard LG refrigerator has an estimated annual energy consumption of 608 kilowatt-hours. That works out to 1.67 kilowatt-hours per day, or 1,670 watt-hours per day.

1,670 watt-hours per day works out to just under 70 watt-hours per hour. If you have a short-term power outage and only need to power your fridge, a 200-watt-hour power station could keep it running for nearly three hours. You'd need a power station with higher estimated watt-hours to run your fridge for longer. A mini fridge would last much longer than a larger model.

Always confirm the electrical requirements for your specific fridge and portable power station before trying this, especially your refrigerator's peak and startup watts.