Brass Rat Statue with offerings in a Hindu temple in Kathmandu (Nepal)
In Hinduism, the rat is Ganesha's Vahana ("vehicle" or "mount"), and some Hindu sects worship this rat.
This lead to the misconception that Hindus pray or worship a Rat God.
In any case, there is nothing wrong in respecting and worshiping any sort of animal.
For more information about the rat as Ganesha's vehicle, read this section of the Wikipedia article on Ganesha: en.wikipedia.org/wiki/Ganesha#Vahanas.