The correct option is
A broken
In the given sentence, the auxiliary 'has' indicates that the sentence is in the present perfect tense. Further, the sentence does not have a main verb and so, the answer must be a verb. Since the tense of the sentence is in the perfect form, the answer must be a verb in the past participle for.
Option A is correct. 'broken' is in the past participle form. Thus, it justifies the fact that the tense of the sentence is present perfect. Thus, it is correct.
Option B is incorrect. 'breaking' is in the continuous form and not past participle. Thus, it cannot be used in a perfect tense.
Option C is incorrect. 'broke' is in the simple past form and not past participle. Thus, it cannot be used in a perfect tense.
Option D is incorrect. 'breaks' is in the simple present form and not past participle. Thus, it cannot be used in a perfect tense.