No, the specific charges of an electron and proton are not the same.

Reason:

The specific charge of a particle is defined as the ratio of the magnitude of its charge to its mass, i.e., specific charge = $\rm \frac{q}{m}$.

The magnitude of the charge of both an electron and a proton are the same and are equal to $\rm | q | = e$. This means that the specific charge is inversely proportional to the mass of an electron and a proton. $\rm specific \ charge \propto \frac{1}{m}$

However, the mass of a proton is greater than that of an electron $\rm ( m_p >> m_e )$. So, the specific charge of a proton is much less than that of an electron.