  When circularly polarized light is scattered from a rotating target, a
rotational Doppler shift (RDS) emerges from an exchange of angular momentum
between the spinning object and the electromagnetic field. Here, we used
coherently spinning molecules to generate a shift of the frequency of a
circularly polarized probe propagating through a gaseous sample. We used a
linearly polarized laser pulse to align the molecules, followed by a second
delayed pulse polarized at 45{\deg} to achieve unidirectional molecular
rotation. The measured RDS is orders of magnitude greater than previously
observed by other methods. This experiment provides explicit evidence of
unidirectional molecular rotation and paves the way for a new class of
measurements in which the rotational direction of molecular reagents may be
monitored or actively controlled.
