Can I sue a restaurant if I find a foreign object in my food?

First of all you did not indicate if you suffered any physical injury from the sharp claw.  In a lawsuit of this type there must be legal fault (ie liability) that would obligate someone to pay, plus some type of injury suffered. Yes there was a defective product but what was the harm done? While ths was no doubt emotionally upsetting for you, it is very difficult to recover for psychological trauma since objectively it's hard to prove that it exists.  How would a settlement number even be arrived at? There are limitations in the law about when you can sue for it. Absent physical injury/illness or medical costs, it is unlikely that you could recover enough money to make a lawsuit worthwhile.

However, you could consult with a personal injury attorney just the same; these type of consultations typically are free.  What you may have better luck with is by contacting the restaurant and seeing if you could get some type of compensation from them.  No business wants bad PR, especially in this economy.

There are two elements to any viable lawsuit. The first is liability, or fault, usually from some negligent (i.e. unreasonably careless) or deliberate act. The second is damages. The legal system is designed to compensate people for out-of-pocket and economic losses, as well as certain non-economic losses (e.g. pain and suffering) which are both very serious and equatable to a monetary loss. Being extremely disgusted, if you were fortunate enough to not be sickened or injured, is not a loss that you can receive compenstation for; there is nothing to sue for.

That doesn't mean you can't contact the restaurant and request compensation, or go to local media and report the incident to give the restaurant bad press. You may even be able to report it to the department of health. There are ways to attempt to get satisfaction. It's just that a lawsuit would not be the correct response.