Each sign has a designated ruling planet. If you want to find out your
moon sign, you need to cast a birth chart, with the time and place of your birth. You can do that at
http://astro.com. Whatever sign the moon was in at the time of your birth, that is your moon sign.
So the moon may not neccesarily be
in Cancer at the time of your birth, although it's possible.
The moon is associated with the emotions, home, family, maternal energies. So anyone born under the sign of Cancer is ruled by the moon.