The rearing of domesticated fowl is called:

In animal husbandry, animals are domesticated, reared and raised for their eggs, meat, fiber, milk, and other food products. 

A piggery is used for rearing pigs.

An apiary is used for rearing bees.

In poultry farming, domesticated birds such as chickens, fowls, ducks, turkeys, and geese are reared to produce meat or eggs for food and trading purposes.

Dairy farming is where cattle are domesticated for milk and milk products.

A fowl is a bird which is domesticated for its eggs and meat. Therefore, this type of rearing comes under poultry farming.