There are no such NASA entrance examination. If you want to work in NASA you need to do a BTech/MTech/MS/PhD in subjects like Aerospace Engineering, Physics, Computer Science and Engineering, Mechanical Engineering and many other fields such as Chemistry etc. After having a good background you can apply for the NASA provided you have some work experience with the space science and after an interview or the way of selection, you will be provided the job.

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