Does "normal torque" exist? Is there any force called normal torque? If a ruler is spinning, and it hits the floor, obviously it will stop. The floor must be exerting a "normal torque" on the ruler. If this exists, please tell me what it is really called.
 A: Torque is not a force. You can say there is a torque caused by normal forces, but there is no special name for that.
A normal force comes from acting with a force on an object resting next to a surface. The surface prevents the object from moving through it by producing a reaction force that is necessarily normal (perpendicular) to the surface (parallel forces are called friction or other such things). Thus the name "Normal" force. For torques, it would not make sense to call something a normal torque. What is it normal to? A torque is always parallel to the axis of rotation, so every torque is just as normal as any other torque.
The closest thing to this would be if you applied a torque to a fixed object. For instance, if you had a see-saw and you pushed up on the end that was in the air, the ground would prevent the other end from rotating through it. When you applied a torque, the ground applied a counter-torque.
This term, counter-torque, might be what you are looking for. Or, at least, the closest thing to it
A: A distributed normal force acting on a body due to contact with another body may be represented by a single normal force acting at the centre of action of the distributed force, but may just as validly be represented by a force-torque pair - i.e. by a force acting at a point on the surface, and a torque.
In the latter situation, the force is a "normal force", and it is not unreasonable to call the torque a "normal torque" - since it is representing, along with the force, a distributed normal force.
In your example, however, you appear to be talking about the moment of a normal force acting on the ruler. Don't confuse the terms "torque" and "moment" - the term "torque" refers to a system of two or more forces that add to zero but produce a net moment on a body because the forces act at different points. 
The normal force acting on the ruler where it touches the ground at one end (assuming that it touches it at a point), has a moment about any given point on the ruler. Such a moment would not be called a "normal moment" - it is simply the moment of a normal force.
You can have "frictional torques", "bending moments", etc., but all of those terms refer to torques/pure moments - i.e. distributed forces that sum to zero but produce a net moment on a body.
