Rat-bite fever is a rare disease spread by infected rodents.
Most people get rat-bite fever through contact with urine or secretions from the mouth, eye, or nose of an infected animal. This most commonly occurs though a bite, yet some cases may occur simply through contact with these secretions.
Symptoms are fairly similar to flu symptoms with the addition of a possible rash.
It would be prudent if you are seeing your healthcare provider about flu-like symptoms, you should mention you have rats (assuming you indeed DO have rats.)
Links:
The CDC
The Rat Fan Club (Debbie Ducommun)