No
As we know that Potential difference along the Electric field = E*d, where E is magnitude of electric field and d is the distance you move along the direction of electric field from some fixed point. Now think if there were a electric field along the surface of Equipotential Surface then as per the equation mentioned above there must be some potential difference thereby the surface will no more be equipotential surface. That is why there is no field along the tangent to the surface of equi-potential surface.