The correct option is
A Have you
In the given sentence, the word 'recently' suggests that the action has been completed. That means that the word 'read' is in the past participle form. Thus, the answer must be either in the past tense or present perfect tense(as it indicates that the action is complete in the present).
Option A is correct. 'Have you' is in the present perfect tense. It grammatically supports the word 'read' being a past participle. Also, it indicates that the action has been completed. Thus, it is correct.
Option B is incorrect. 'Do you' is in the present tense and does not support the fact that 'read' is a past participle. Thus, using it will make the sentence grammatically incorrect.
Option C is incorrect. 'Does you' is itself grammatically incorrect. The auxiliary 'does' is only used with third person singular pronouns whereas, 'you' is a second person singular pronoun. Thus, it cannot be the answer.
Option D is incorrect. 'Are you' generally indicates present continuous tense. Thus, it indicates that the action is ongoing and not complete and so, it is incorrect.