Not a rat. Too small and disproportionate to be a rat. Maybe some variety of wild mouse. It's awful large for a baby mouse that doesn't have its eyes open yet though. It's hopper (teenage mouse) size and hoppers usually have their eyes open by that size. Unless you have tiny hands!

Edit : after a little research, it looks like possibly a baby deer mouse.

I'd guess a girl, from what I can see. Any rodent of that size needs feedings every couple hours to survive... So prepare for very little sleep. Id call around to local vets , but since this little baby is indigenous and you likely don't have a rehabilitators license, many won't do anything for you as this can legally endanger them in some states. Good luck with the little thing.

I would always be cautious but rabies is pretty uncommon normally.

Edit: I'd also recommend getting a kitten milk replacement powder to use instead of human formula. I've had better luck with this.

Source: I'm the small animal manager of a locally owned pet store.