Besides stalking, according to the charge sheet filed by the Delhi police, the four students were also booked on charges of stalking, criminal intimidation and intention to insult the modesty of a woman.
The final report was filed before Metropolitan Magistrate Snigdha Sarwaria who took cognisance of the chargesheet and put up the matter for October 15, news agency PTI reported.
"I take cognisance of the offence as mentioned in the charge sheet. Considering the overall facts and circumstances of the cases, there is sufficient material on record to issue summons against the accused," the judge said, noting that the accused were on bail.
In April 2017, the police had alleged that the drunk students, identified as Sitanshu, Karan, Avinash and Amit, had followed Ms Irani's car in Lutyens' Delhi, following which they were detained.
The students, in the age group of 18-19 years, were detained at the Chanakyapuri police station in the diplomatic enclave. The incident had occurred near the US embassy, the police had said.
The medical examination of the accused had confirmed the presence of alcohol in their blood.
(with inputs from PTI)