Rats can't throw up, that's why rat poison works.
Rats don't really need to throw up anyway. Their digestive systems are powerful enough to process what would normally be dangerous materials, and their heightened senses of smell and taste keep them from consuming anything that they can't digest.
Vomiting is actually a complex process that rat's don't have the proper hardware to do. (They also can't burp or have acid reflux!) Rats can "regurgitate" their food, that is, they can push food from their stomach to their esophagus. Vomiting is a forceful expulsion of stomach contents and it requires the contractions of muscles that rats don't have. For animals that have the ability to vomit (like humans), vomiting serves an important purpose. It's an automatic response to consuming poison, which keeps the animal alive. Rats have strong resistances to poison, but since they can't vomit, if they ingest a lethal amount of poison, they will die.