Electrons and protons carry charge as well as mass, so they exert both vanderwaals force as well as gravitational force, but the strength of electrostatic force would be very large than gravitational force.
Consider two charges 1 coulomb each separated by a distance 1 meter in space is will attract or repulse with a force of 9×109N while two masses each of 1kg separated by a distance 1m will attracted by a force of 6.67×10-11N. That is gravitational force is much weaker than electrostatic force.