According to online resourses, ISRO recruits scientists if they have a PhD in astronomy, mathematics, or physics. Along with this, the candidate must hold an engineering degree. You can opt for polytechnic and lateral entry into BTech after that, but lateral entry will close the gates of reputed institutes like NITs and IITs for you. So it will be better to give the JEE after class 12 or after you complete your polytechnic. The recruitment is conducted by the Centralized Recruitment Board. Selection is based on the written exam and interview.