Rat traps that are designed to snap a rats neck certainly could break a finger if you get your finger caught in one.
It's very easy to get your finger caught in a rat trap while setting the rat trap so be careful if you do need to set out a rat trap.
My brother broke his index finger a few years ago while setting out a rat trap and it hurt him and he had to go to the emergency room to get his broken finger splinted and fixed.
Smaller mouse traps are designed to break a mouses neck which requires less force and is unlikely to break a human finger.
I've gotten my finger caught in a regular small size mouse trap and it just hurt but it didn't break my finger.
But a mouse trap is much more powerful and can indeed break a human finger so be careful when putting out and setting up rat traps.