how do I deal with a coworker who is rude to me?

First you need to tell them to stop, if that doesn't work, please contact HR or your boss and let them know the situation. If that does not solve it either, contact the higher authority at the main headquarters.

Relate the facts of the incident where coworker had been rude, and say the behavior caused me to feel disturbed and uncomfortable, and asked if it was something I did or said that caused such reaction.

I would let my co-worker know that their words sounded rude to me. How their words made me feel. I would also remind them of our workplace policies that are in place to make all employees feel safe and how I would have to follow those guidelines if their actions continued. I would also like to hear them explained their intentions in saying the offensive words because sometimes what we hear and what a person wanted to say are lost for many different reasons. A warning is always appropriate the first time an offense is done. We all have made mistakes