Depending on how old he is (how big is he? are his eyes are open? fur?) I would syringe him some water.

What makes you think he is dehydrated?

If he's really a newborn, and he didn't have his mommy to nurse off of, you should've been syringing him formula anyways. I forget what kind is suggested. Again, depending on his age, I'd take him to a vet (usually, they'll put you on a payment plan if you're having money troubles) - they can tell you specifically how to help him. Once they're a certain age, they don't mind giving him a shot of "gatorade without the sugar" (that's how my vet explains it).

Other than that, I don't know what else you can do. Don't force a ton of water/formula down him, and don't let it be TOO cold.

When you say you rescued him from your backyard, what do you mean? Was he in a nest and you took him out? Or was he walking around and stuff, alone? Was there a nest around, or any sign of another rat? And, are you sure it's a rat?

No offense to you because I know you're just trying to help, but sometimes it really irks me when people "rescue" animals and don't know what the heck they're doing. I'd like to know how old he is, or a picture so I can tell about what age, because I don't know how he just got dehydrated.. were you nursing him? Or giving him a water bottle to drink from? Where is he currently living? Does he have an "opportunity" to drink whenever he feels like it, or is he just too young?