What is the procedure of joining Indian Army after B.Sc.

Hi Buddy,
you can definitely apply for the Indian army after completing your graduation to become an officer in the Indian army
To get admission for this you have to clear the CDS exam conducted by UPSC twice a year.

Through this exam you can directly get the officer category post, the eligibility criteria and other related details regarding the exam is given as below:-

The eligibility criteria for this are:
age limit :-between 19-24 years
qualification :-graduation
physically and medically fit
height minimum 152 cms and weight proportionate to that
nationality Indian
Marital Status :-unmarried

If you qualify all these criteria you can apply for CDS exam after this you will have SSB interview and then medical board.
If you clear all these you will be given training to become an officer in the Indian army
So concentrate on your studies now .
All the best