Is it possible to get strep throat if you don't have any tonsils?

Yes: Even in the absence of tonsils, you can still get a strep infection.

Yes: A tonsillectomy removes the prominent palatine tonsils on either side of the back of the throat. However, there is tonsil like tissue located in patches around the throat and roof of the throat. That and the rest of the throat tissue can become inflamed with a strep infection. Removal can reduce the intensity of symptoms but does not eliminate the risk of strep.