If you want to take admission in IIT's for BTech course then you have to qualify the JEE MAINS and JEE ADVANCED. The JEE MAINS can be given for 3 consecutive attempts and JEE ADVANCED can be given for two time i.e., On the board appearing year and 1 year post board examination. Thus after graduation you can't join IIT for BTech courses but you can join for Masters.

If you do graduation in Engineering then by qualifying GATE you can admission in IITs for MTech courses. If you do Bachelors courses such as Physics, Chemistry, Mathematics, Statistics, Economics,  Biotechnology (BSc/BTech) then for MSc program you can apply for IIT's via IIT JAM examination. Now if you want to do PhD then also you can apply for IIT's by qualifying NET examination or JEST.

So yeah! You can join IIT's for PG courses after Graduation.

To know more about IIT JAM visit the link below:

https://university.careers360.com/exams/jam

To know more about GATE visit the link below:

https://engineering.careers360.com/articles/gate

I hope this answer helps. All the very best for your future endeavors!