Hey,
Space and rocket engineering come under the *Aerospace engineering*.

•Aerospace engineering is the primary field of engineering concerned with the development of aircraft and spacecraft.
It has two major branches-:
•Aeronautical engineering
•Astronautical engineering

Yes, there are four IITs which offer bachelors in aerospace engineering:

• IIT Kharagpur
• IIT Madras
• IIT Bombay
• IIT Kanpur
 
Hope it helps!

According to your interest, The best college for this course for you is BITS MESRA. There has a course named Department of Space Engineering and Rocketry

In IIT'S, you should got aerospace engineering. This is also related to space engineering & rocketry but not actually it is that you want!!

IIST THIRUVANANTHAPURAM & Indian Institute of Aeronautics, patna also best for aerospace engineering...

According to your course of interest, I think you should go for BITS MESRA...