No, if you put a cat on the moon not only would it not make it home, it would die.
Improved question, improved answer.
Cats have impressive memories for directions that often enable them to find their way home after travelling long distances. This superior navigation ability is believed to derive from two things: using the angle of the sun for navigation (which can be done even on cloudy days because the cat uses polarized light for wayfinding) and being sensitive to the Earth’s magnetic fields. This latter hypothesis was borne out when it was found that attaching a magnet to a cat will disrupt his navigational skills.
A story that dramatically illustrates the phenomenal feline navigational ability is that of Howie the Persian, who crossed 1,000 miles of brutal Australian outback to find his family. Howie had been left in the care of his owner Kirsten’s grandparents while Kirsten went on an overseas trip, but had disappeared from their home while Kirsten was away. A year later, a mangy stray showed up on Kirsten’s doorstep. Upon cleaning up the filthy, skinny, injured animal, they realized that it was Howie, who had fought his way back through a vast expanse of harsh desert and wilderness to return to the family he loved.
Source: Cat Facts, by Marcus Schneck and Jill Caravan. Barnes & Noble Books: 1993.