Can single force acting on a rigid body lead to rotational motion? Can a single force acting on a rigid body be the  cause of pure  rotational motion of the body? Suppose a single force acts on a disc in space at rest at a place other than its COM would the disc show both translational and rotational motion?
 A: It is always true that:
$$ F = \frac{dp}{dt} \tag{1} $$
and:
$$ \tau = \frac{dL}{dt} \tag{2} $$
where $F$ and $\tau$ are the (net) force and the torque, and $p$ and $L$ are the linear and angular momenta. So if you apply a force it must change the linear momentum in accordance with equation (1) i.e. you cannot have pure rotational motion.
A: 
Can a single force acting on a rigid body be the cause of pure rotational motion of the body?

Yes. Assume that the body starts with some linear momentum $\vec p$ but no rotational motion. And suppose that we apply a force $\vec F =-\vec p/t$ for a time $t$. Then the body will end with no translational motion and if $\vec F$ is applied off center then it will have some rotational motion.
A: 
Can a single force acting on a rigid body be the cause of pure
rotational motion of the body?

You can only produce pure rotation with a couple. A couple consists of two equal and opposite parallel forces.
A single force whose line of action is not through the center of mass will produce rotation plus translation.
A single force whose line of action is through the center of mass will produce pure translation.
See the figures below.
Hope this helps.

