Dear Student,
The direction of electric current is opposite to the direction of the flow of electrons. The flow of electrons and current are directly related. Current will only be produced when electrons flow. That is why current is defined as the flow of electrons or charge carriers. Protons do not flow in an electric circuit; they stay fixed in place because they’re much heavier than the electrons.
So the current inside a conductor is due to electrons and not due to protons. So even if they are stationary then also electric current will flow if electrons are free to move in a definite direction.
Regards