They have their own equipment, rules, competitions, and more. Here's some info from their website:
Rat Agility is much like dog or cat agility only the equipment is rat sized. Fancy or Pet Rats are very affectionate and intelligent animals. They are as far removed from their wild cousins as a wolf is from a dog. Rats can be taught tasks, tricks and behaviors. More and more people are keeping rats as pets so Rat Agility just makes sense. And, (smiling as I write) the equipment for rats is easier to transport and is easier to build and store then the equipment for dogs and cats.
I have found, over and over, with many different ratties I have trained to do Rat Agility, that the animals love the equipment, the tasks and the fuss made over them for doing it as well as any treats they may receive....but mostly they love spending time and interacting with their trainer.