It could be a nice hunting trophy, but it smells too bad to place it on a wall. On the other hand, it demonstrates that owner is capable of killing rats, even big and smelly ones. This skull has special properties related to rat control.
When equipped, provides the “Ratter” buff which:
The Giant Rat Skull is a quest item that's part of the Ghost's questline. It represents an alternative path in the sewers quest where the player hunts a special Fetid Rat instead of collecting 8 regular rat corpses. When equipped, it provides a useful effect against rat-type enemies.