Most institutes do not offer courses in Genetic Engineering as a special discipline but as a subsidiary in biotechnology, microbiology, biochemistry streams. Genetics is offered at the undergraduate level, at Kakatiya University, Warangal and Osmania University, Hyderabad, both in Andhra Pradesh.
Some of the universities which offer genetic Engineering courses at postgraduate and doctorate levels are the Bio-Informatics Centre of Jawaharlal Nehru University (JNU),New Delhi, Indian Institute of Technology (Kharagpur and Delhi), Delhi University, University of Calcutta, MKU-Coimbatore, Birla Institute of Technology (Pilani Rajasthan), University of Lucknow, Jadavpur University (Kolkata, West Bengal) etc.
And in order to be eligible for an under-graduate course you will have to give the engineering CET and at Post graduate level the universities will have their own entrance exams.
Hope this helps.