The answer to your question really depends on what job you are looking for at NASA. Like most large federal agencies, it employs a wide range of employees, from janitors to astronauts. If you want to be a Civil Service employee assigned to NASA, you will need to pass a Civil Service exam. However, if you want to be an astronaut, your resume, including education, will undergo exhaustive scrutiny before you ever hear from NASA. Since NASA was launched, it has trained only about 330 astronauts with impressive credentials and often military backgrounds. They undergo rigorous mental, physical, and informational training. NASA currently is not recruiting astronauts.
You must apply through the USAJOBS website.
Good luck with your career goals!