If if the wall or vertical surface is rough enough then yes both Rats and Mice can climb up the wall.
I've seen a Rat in my house last year climb up a wall.
Rats can also climb up drain pipes especially when the drain pipe is near a wall.
If you have rats in your house you should get some Rat Traps to kill the rat as Rats can spread diseases and cause destruction in your home.
If you have no children or pets the best thing to do is set out rat poison which will kill the rat although you'll have a stinky odor if the rat dies in or near your home.
But the odor will eventually go away within a week or two once the Rats body has fully decomposed.