You have Three options to become a research scientist/engineer at ISRO
1)Get recruited into ISRO as Scientist/Engineer by one of the following three ways.
a. Get admission in IIST for B.Tech (or M.Tech) in the branches it offers. Maintain good academic record and if there are requirements you will get absorbed in ISRO
b. ISRO recruits some freshers in campus drive from some IITs and NITs.
c. Complete B.E./B.Tech from any other AICTE approved college in India, give ICRB's exam for Scientist/Engineer for your stream, clear the interview and get into ISRO.
2) Get selected as Junior Research Fellow (JRF) and if possible continue working as Scientist/Engineer.
3) Apply after completing your PhD.
Congrats & All the Best for your Future.