I know you--- a member of Green Club for half a year.

C
后面有for half a year,所以是现在完成时,因此排除A,而可以说是joined in a club,不能说joined a member,所以D也排除了.不能用become说变成了一员,这是中式英语,B也排除.所以选择C.
这句话的原型可以这样说,He is a member of Green Club.is变形为have been.