In addition, since people put out poison for rodents, any cat let outside who hunts is at risk for being poisoned from eating a poisoned rodent. Death by rat poison is a horrible horrible death. They bleed to death. From the inside.
Cats are hunters by nature. Cats are also instinctual family providers, so will bring you their kill to share, as you have happily discovered. It's a high honor, being provided for by your cat.