An unresolved issue in the theory of liquid crystals is the molecular basis of the electroclinic effect in the smectic-A phase. Recent x-ray scattering experiments suggest that, in a class of siloxane-containing liquid crystals, an electric field changes a state of disordered molecular tilt in random directions into a state of ordered tilt in one direction. To investigate this issue, we measure the optical tilt and birefringence of these liquid crystals as functions of field and temperature, and we develop a theory for the distribution of molecular orientations under a field. A comparison of theory and experiment confirms that these materials have a disordered distribution of molecular tilt directions that is aligned by an electric field, giving a large electroclinic effect. It also shows that the effective dipole moment, a key parameter in the theory, scales as a power law near the smectic-A--smectic-C transition.