Dear student,
Robotics engineering is the combination of electrical, mechanical and computer science branch.
To take admission in this course you will have to apply for JEE conducted by IIT.
Eligibility criteria :
Academic qualifications -
Should be passed out in 10+2 with science stream from a recognised board
Subjects in 10+2 should be physics, chemistry and mathematics.
Compulsory subject should be English.
Optional paper should be computer science.
Passed in all the subjects individually.

Marks-
General category - 75% in 10+2
Reserved category - 60% in intermediate.

Age-
Candidates who apply shouldn't be of more than 25 years of age.

Best institutes for robotics course in India are:
Centre for Artificial intelligence and robotics,  Bangalore
University of engineering,  hyderabad
Jadavpur university,  West bengal
National institute of technology,  kurushetra
Indian Institute of technology,  roorke
BITS Pilani, rajasthan
Amity university,  uttar pradesh.

All the best dear. I hope i was able to satisfy you with my answer.