A dipole in an electric field can experience torque, but there is an equilibrium position with no torque. Considering a field due to a positive point charge, if you have a length of material with two dipoles at each end, the positive end will tend to repel, and the negative will tend to attract. If the dipole is not parallel to the electric field lines, there will be some net torque. In the position where the dipole-object is parallel to the electric field lines, with the negative dipole close and the positive dipole farther away, if both charges of the dipole have the same magnitude, there will be not torque, but net movement towards the point charge. If the object is flipped, such that the positive end is now closer, the object will be repelled on the whole.
So yes, they can spin. If you consider net movement, that's probably a more complex question. Assuming a dipole with the same charge magnitudes, it will move in an electric field due to a point charge. In a uniform electric field, such a dipole will not move.
Just for MCAT purposes though, I would not bet on this being tested. I have yet to see a practice question or passage about this topic.