Light that carries linear or angular momentum can interact with a mechanical object giving rise to optomechanical effects. In particular, a photon transfers its intrinsic angular momentum to an object when the object either absorbs the photon or changes the photon polarization, as in an action/reaction force pair. Here, we present the implementation of light-induced selective resonant driving of the torsional mechanical modes of a single-mode tapered optical nanofiber. The nanofiber torsional mode spectrum is characterized by polarimetry, showing narrow natural resonances (Q$approx$2,000). By sending amplitude modulated light through the nanofiber, we resonantly drive individual torsional modes as a function of the light polarization. By varying the input polarization to the fiber, we find the largest amplification of a mechanical oscillation (>35 dB) is observed when driving the system with light containing longitudinal spin on the nanofiber waist. These results present optical nanofibers as a platform suitable for quantum spin-optomechanics experiments.