How can Torque act on an electric dipole if an electric dipole is not a rigid body? According to my knowledge of physics, torque can only exist on a rigid body and an electric dipole is defined as a "system of charges" (equal in magnitude, opposite in sign) separated by an infinitesimal distance.
clearly, we can't call a dipole as a "rigid body", since it's just a system of particles, so how does torque act on it when a dipole is placed in, say, a uniform electric field? shouldn't the individual charges just start separating away from each other?
 A: 
shouldn't the individual charges just start separating away from each other?

If the field is strong enough, certainly. But keep in mind that there is an attraction between the oppositely charged particles. Just imagine two balls connected by a somewhat elastic string that will break if the force applied to it becomes too large. This system would align with any external forces, but if the external force is too large the balls will separate.
Of course the ideal dipole is an idealization, but if the external fields are not too strong, then we can treat the dipole as a rigid body, since the change in separation in the charges should be negligible in effecting the dipole moment or the torques involved.
A: Electric dipoles are charges separated from one another, but they can reside on a molecule that maintains the separation. An example is a water molecule. The arrangement of the Oxygen and two Hydrogen atoms is such that the molecule is more positive in one area and negative in another area, that is, the charge distribution is asymmetric, though the molecule as a whole is neutral.
As far as torque goes, the water molecule will experience a torque if placed in an electric field as the molecule will attempt to align with the field. This will not cause charge to separate. This is the basis for microwave cooking. The alternating electric field of the microwaves applies an alternating torque to the water molecule making it rotate and giving it rotational kinetic energy. That, in turn, raises the temperature of the water.
Hope this helps.
A: "torque can only exist on a rigid body" is not true.
Torque=RXF, and does not depend on the type of body it acts on.
Your definition of 'dipole' does not say the charges are not held together, so they won't
"start separating away from each other".
Even if they separated, their angular momentum would increase due to the torque. 
