Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. ... In some cases, theoretical physics adheres to standards of mathematical rigour while giving little weight to experiments and observations.

Can I be a theoretical physicist?

No; anybody can be a theoretical physicist. You only need to be interested in the subject and determined to work hard.

Does NASA Need theoretical physicist?

Yes, you can work for NASA while being an astrophysicist/theoretical physicist. They employ people from a variety of professions, not just aerospace engineers and astronauts.