Most spiders, especially small house spiders, are generally harmless to cats.
However, any poisonous spider that can harm people can also harm your cat.
Poisonous spider bites can cause major illness or even death.
Some bites cause localized reactions that turn into major wounds.
Others, like that of the Black Widow, cause vomiting and diarrhea, paralysis, drunken gait, and muscle tremors.
Suggestions
If you suspect your cat has been bitten by a poisonous spider, get to the veterinarian right away.
If your cat ingests a spider, the venom is unlikely to be a problem, as the stomach acids tend to counteract the venom.
However, you should still observe your cat closely for a day or two in case any signs of illness appear.
Note: even if labeled as safe, any food can potentially cause allergies. When introducing a new food, please feed a small amount and observe your cat for any allergic reactions.