No, the summation of all the forces acting on the body zero does not mean that the torque produced by these forces is also zero.
Rotational and angular motion can be produced even when the external forces acting on the body is zero.
For eg., When a fan is switched on, the centre of the fan remains unmoved, while the fan rotates with an angular acceleration. Since, the centre of mass of the fan remains at rest, the vector sum of all the external forces acting on the fan is zero.
