The number of protons in an atom defines its atomic number. Carbon, by definition, has an atomic number of 6. Therefore, a neutral atom of Carbon-13 will have 6 protons.

The "13" in ¹³C refers to the atomic mass, which is the total number of protons and neutrons in the nucleus. This tells us that ¹³C has 7 neutrons, but the number of protons remains constant for all isotopes of Carbon.