We present measurements of the polarized extinction of gold nanorod suspensions exposed to an external electric field. By employing an amplitude modulated field in combination with lock-in detection we resolve changes in the optical density as low as 10(-6) in an integration time of 10 s. This sensitivity allows us to probe the partial alignment of small gold nanorods with an aspect ratio of 2.5 and a width ranging from 13 nm to 28 nm. The degree of orientation scales as the square of the electric field strength, as expected for an induced dipole moment in an external field. By varying the modulation frequency we measure the rotation diffusion constant of different samples, which are in excellent agreement with the calculated values for a short cylinder.