Cat just delivered this to me, but it looks “off” for a rat to me. Face too blunt. Tail and ears maybe not right. Body seems short.
A vole?
Not a rat.
I think so, but I can not see the tail.
More photos in the link.
If you click on it you can see the tail in the other photos.
I concur then, Vole.
Yep, looks like. First one I’ve ever seen here, I think. Much bigger than the usual shrews the cats bring home.
Don’t you hate that, I mean could they mix it up a little?
How about a nice trollop or a fishwife for a change?
Hispid Cotton Rat
A fat rat. Good Kitty!
Voles are much smaller than rats. They are related to hamsters and are similar size.
It isn’t a Norway rat (most common type of city rat). They have pointier noses and are quite large.
It could be a pack rat, Neotoma species. There are many native pack rat species.
There are so many rodent species that one would need to know your location and be a bit of a rodentologist to know exactly what your cat brought in.
Have you tried asking your cat?
I think this nailed it, though I don’t know about the specific variety. They are referred to simply as cotton rats by us unwashwed 
Too polite to talk with her mouth full.
That’s a change, then: When I was growing up with cats, I became quite familiar with the sound of a cat talking with her mouth full.
Definitely not a rat as most of us understand the term. Looks like a vole to me. But it would be good to know the location. Did you take this picture in North America? Can you be more specific as to where?
BTW, the character “Rat” in the English children’s novel “The Wind in the Willows” is actually not a rat of the kind we all know (that is, either a Brown Rat - Rattus norvegicus or a Black Rat - Rattus rattus) - he is actually a European Water Vole.
Anderson County South Carolina, which is in the foothills of the Appalachian mountains, bordering with Georgia. (I could give GPS coordinates, but that’s probably more specific than necessary.
Going from the picture, I think it could be a Meadow Vole (Microtus pennsylvanicus).
I’m doubling down on Cotton Rat then.