The correct option is B to have
The infinitive verb is a verb with the word 'to' in front of it. This verb is always just a verb. There is no - ed, no - ing, no - s at the end of the verb. Thus, options A, B and D are wrong according to the rule. The correct option is C since 'to' is used in front of the verb 'have'. Hence, sentence would become: He appeared to have cast his vote in favour of us.