You'd have to have larger rats for them to be worth "farming" - I am not sure whether a diet of grain would be enough with the more common species. Also, given the intelligence, dexterity, and social characteristics of rats, it might be difficult to "harvest" them unless you put them in a very august, stone-lined compound with few places to hide. After all this, two visions come to mind:
- Rats are never seen as a delicacy, but instead end up at state fairs served deep fried and on a stick
- PETA lodges complaints about the shocking conditions in which rats are raised for the slaughter