The petition was filed by vice president of Vipra Foundation's youth wing, Rajkumar Sharma, over a photo shared by Dorsey in which he posed with women holding a placard reading 'Smash Brahminical Patriarchy'.
The photo was taken during Dorsey's recent trip to India.
"Metropolitan Judge Rachan Bissa has admitted the petition and listed the matter for hearing on December 1," the petitioner's counsel H M Saraswat said.
Sharma said the post was "anti-Brahmin" and used coarse language, which was humiliating and thus, intolerable for the community.
Twitter has tendered an apology in the matter and said the post did not reflect its views or those of its CEO.
Sharma said Dorsey had not apologised.
Even if he apologises, it would not mitigate his crime, he added.
Saraswat said the petition has been filed under various sections of the Indian Penal Code, including 295 A (deliberate and malicious acts, intended to outrage religious feelings), 500 (defamation) and 120 B (criminal conspiracy).
"He (Dorsey) has committed the crime of triggering hatred for a community and we would proceed against him in the court," he added.