A mystic is not, strictly, an office at all: a mystic is recognised rather than appointed, one whose account of direct experience of the divine is accepted by a tradition.
Experience, not office
What defines the mystic is the claim to a direct, immediate experience of the divine or the ultimate, an encounter or union beyond the ordinary reach of doctrine and rite, and this is a matter of experience and its reception rather than of any position conferred, so no one is ordained a mystic. A tradition may come to accept a person as a genuine mystic on the strength of their life, their teaching and the fruits of their experience, but the recognition follows the experience rather than granting an office.
Within and across traditions
Mystics appear in every major tradition, the contemplatives and visionaries of Christianity, the Sufis of Islam, the Kabbalists of Judaism, the realised sages of the Indian traditions, and their accounts of direct experience have often stood in a delicate relation to the institutional authorities, sometimes revered, sometimes suspected, since a claim to immediate knowledge of God can sit uneasily with a religion of doctrine and hierarchy. The comparison of mystics across traditions has been a major theme of the modern study of religion, some scholars stressing a common core of experience and others the shaping of each experience by its own tradition. The mystic is thus less a role than a recognised standing, granted to those whose reported experience of the divine a tradition comes to accept.