Final answer:
In 'Ender's Game,' Mazer Rackham replaces Graff as the head of the battle school. He plays a crucial role as Ender's mentor in the latter part of the story. The answer is option C.
Step-by-step explanation:
The character who replaces Graff as the head of the battle school in Orson Scott Card's science fiction novel 'Ender's Game' is C. Mazer Rackham. In the narrative, after Graff is promoted, Mazer Rackham takes over the role of running the Battle School, which is the advanced military training facility for children showing exceptional tactical and strategic abilities. Mazer Rackham is a key character, who later becomes Ender's mentor and prepares him for the ultimate battle against the alien race known as the Formics.
Hence, the answer is option C.