We demonstrate experimentally a method of varying the degree of directionality in laser-induced molecular rotation. To control the ratio between the number of clockwise and counter-clockwise rotating molecules (with respect to a fixed laboratory axis), we change the polarization ellipticity of the laser field of an optical centrifuge. The experimental data, supported by the numerical simulations, show that the degree of rotational directionality can be varied in a continuous fashion between unidirectional and bidirectional rotation. The control can be executed with no significant loss in the total number of rotating molecules. The technique could be used for studying the effects of orientation of the molecular angular momentum on molecular collisions and chemical reactions. It could also be utilized for controlling magnetic and optical properties of gases, as well as for the enantioselective detection of chiral molecules.