B

Step 1: The torque \( \tau \) on a dipole in an electric field is given by the equation \( \tau = \mathbf{p} \times \mathbf{E} \).
Step 2: In stable equilibrium, the angle between the dipole moment \( \mathbf{p} \) and the electric field \( \mathbf{E} \) is \( 0 \) degrees (aligned).
Step 3: When the dipole is rotated by an angle \( \theta \), the torque can be expressed as follows:
\( \tau = pE \sin\theta \) (since the torque depends on the sine of the angle).
Step 4: Therefore, the torque required to rotate the dipole from the stable equilibrium position by an angle \( \theta \) is \( pE \sin\theta \).
Thus, the correct option is B.