if I went to eat at a restaurant and got food poisoning can I sue?

the short answer is yes.  The more practical answer is that it might be very difficult.  Proving the illness came from the restaurant is hard.  Even if you cna prove it, your damages are limited to the medical expenses, lost wages, etc. you experienced as a result of the illness and any pain suffering and mentakl anguish experienced during the odeal.  Obviously the worse it was the more damages you can recover.  Assuming the effects were temporary, these cases aren't usually worth that much on a single case basis.  That makes it hard for the injured party to find a lawyer because it usually isn't worth paying an attorney on an hourly basis and most lawyers won't take a case like this, again assuming the effects were temporary, on a contingent basis.   These cases are most often successful when multiple people become ill from the same establishment.  They are easier to prove and the damage model greatly increases.

The first question is what are your damages?  The second question is how do you know the place you ate caused the food poisoning?  I would encourage you to seek the advice of a personal injury trial lawyer to discuss the matter if you choose to pursue the matter.