The correct option is A put / up
To "put someone up" is to have someone over as a guest to stay in a place that is not their home. Thus, according to the context, the stay of a guest in the extra room of the house is to "put them up". Therefore, option A is correct.
To "put someone off" is to make someone not want or like something.
To "put someone through" is to connect them for a conversation on the telephone.
To "put someone in" is to elect someone or to give them responsibility.
Thus, here option A is the correct answer.