That wouldn't even work.. Think about it.. A rat would chew through just about anything it was tied with in seconds. If there is a way out of a situation, a rat will find it.
Besides, like Jerry said, even if you could restrain a rat for any period of time by simply tying it down, it would panic so much that once it was caught it would be much more likely to bite.
Inhumane, and ridiculously silly idea.