An official said a video clip, in which a half-naked Haq was seen in the company of the girl in a hotel room, had gone viral on the social media.
Accused Maulana Anwar-ul-Haq, who is a cleric in the Jama Masjid in Chah Siri, had earlier announced a reward of Rs 51 lakh to anyone who cut the tongue of Hindu Mahasabha leader Kamlesh Tiwari for the latter's disparaging comments against Prophet Muhammad.
The comments had led to violent demonstrations in many parts of Uttar Pradesh.
The girl claimed she was taken to the cleric as her family felt she was under the influence of some evil spirits.
She accused Haq of raping her on August 24 night on the pretext of conducting a physical examination. She along with her family members later assaulted Haq.
A case of rape and conspiracy to harm the victim has been registered. A police official said efforts were on to arrest the accused.
Informed sources said Haq was trying to arm twist the police by claiming proximity to Chief Minister Akhilesh Yadav.