A

Step 1: The torque \( \tau \) acting on a dipole in an electric field is given by the formula:
\( \tau = \mathbf{p} \times \mathbf{E} \)
where \( \mathbf{p} \) is the dipole moment and \( \mathbf{E} \) is the electric field.

Step 2: The magnitude of the torque can be expressed as:
\( \tau = pE \sin(\theta) \)
where \( \theta \) is the angle between the dipole moment and the electric field.

Step 3: If the dipole moment is aligned parallel (\( \theta = 0^{\circ} \)) or anti-parallel (\( \theta = 180^{\circ} \)) to the field, then \( \sin(\theta) = 0\) yielding a torque of zero.

Therefore, the torque acting on the dipole when it is aligned with the electric field is zero. Thus, the correct answer is option C.
Therefore, the answer is A.