I'm going to be short with my girlfriend because I'm upset at her for Facetiming me at 4 am.
Why do you want to be short with her?
Because I was almost asleep but she decided to Facetime me.
It is understandable that you are upset for being woken up at 4am. But yelling back at your girlfriend is not the way to resolve the issue.
How should I resolve it then?
I think you should let her know that you were trying to get to sleep, and that 4 am isn't a good time to talk. I'm sure she'll understand where you're coming from.