Can you sue a caucasion person for calling you the N word?

That type of behavior is horrible and uncivilized, and I'm sorry that you were treated so rudely. Unfortunately, my sense is that this incident, standing on its own, would not give you a legal claim. I'll bet that the person who treated you this way will get what he deserves in the end. Good luck.

Unfortunately, there is cretins living in this world. That does not mean that every stupid, offensive thing we encounter is the basis for a lawsuit. Sometimes it is better to leave the morons to their own swill and go on to live one's own life. Sorry you had to deal with that.