Control of the orientation of the angular momentum of linear molecules is demonstrated by means of laser polarization shaping. For this purpose, we combine two orthogonally polarized and partially time-overlapped femtosecond laser pulses so as to produce a spinning linear polarization which in turn induces unidirectional rotation of N2 molecules. The evolution of the rotational response is probed by a third laser beam that can be either linearly or circularly polarized. The physical observable is the frequency shift imparted to the probe beam as a manifestation of the angular Doppler effect. Our experimental results are confirmed by theoretical computations, which allow one to gain a deep physical insight into the laser-molecule interaction.