Hello

Your best bet is to take up Aerospace Engineering, since it is a course that is rarely offered and also because those who graduate are hard to find [migration, higher studies, etc]. 
Engineers from other branches are comparatively much easier to find. 
The other branches that you may apply for, in descending order are Mechanical, Electronics, Computer Science and Civil.  
Please note that whichever branch you pick, you must be the best at what you do. You must excel in class and graduate with top marks, and consistently so. 
And one last thing, no criminal record of any kind, be it jumping signals or public nuisance.

Thank you and all the best.

Aerospace engineering is the best engineering to get job in isro. Isro is a awesome place to work . Branches like computer science engineering , mechanical , civil, electrical communication  engineering are also best for getting  job in isro. Good luck .

Dear,

The eligibility criteria to get into ISRO is:

Eligibility for ISRO:-

1.The candidate must have complete the B.tech/BE in the streams like- Electronics/Electrical/Computer science/Mechanical.

2.The candidate must have secured 60% + aggregate through out the career.

3.The candidate age should not be more than 35 years for Gen. / OBC 38 years / SC/ST 40 years.

One can have a b.tech degree in Electronics/Electrical/Computer science/Mechanical.

But according to me Mechanical engineering would be the best.

Hope this helps. All the best!

Dear aspirant,

      I really appreciate your interest to work in ISRO. However the recruitment for ISRO is done in many ways. ISRO has annual intake of engineers and scientists as well.....

Though there is a specific exam for the intake but they highly prefer on the merit of the student rather than the degrees completed by the candidate. So, you must have good knowledge in your subject and general steps to remember are,

You have to complete your b.tech with good percentage (i.e.., an aggregate of more than 65%) 

You can be a student from branches such as Aeronautical engineering, Aerospace Engineering, Electronics and communication engineering, Computer science and engineering, Electrical and Electronics engineering, etc...,

Good luck and hope for the best !!

Wishing you all success !