I'd say you should just set it free - it'll be able to take care of itself unless it's a tiny baby that hasn't even opened its eyes [and I see that it's older than that, judging by that picture]. I suppose you could keep it, but I can bet that the animal wouldn't be too happy in captivity or do well considering it's been living in the wild for a while now. The only stories I've heard of people successfully keeping wild mice/rats, or any animals really, in captivity is if they were found at quite a young age, often times before they've even opened their eyes. And unless you have experience and/or have done your research [looking basic information up on google doesn't really count], it could end up dying pretty easily, and quickly.
But I know what you mean, our cats have brought up little tiny mice/voles too. ;u; they are pretty adorable, and even though it may be tempting to keep it, I'd think that it's best not to.