Can you become a rocket scientist with a physics degree?

Rocket science is a combination of a lot of different things, and it depends exactly on what you want to do. Many rocket scientists are mechanical engineers with emphasis on fluid dynamics or aerospace. In physics, you would most likely specialize in astrophysics, since that would help you gain expertise in relativity, gravitation and a little bit of particle or plasma physics needed to understand how real objects in space work. You might be responsible for figuring out communication delays and distortion due to relativistic and gravitational effects, or for figuring out computer system stability in radiation-rich environments like space, or figuring out the best orbital path that would be collision free and require as little use of thrust as possible.