Radiation pressure is associated with the momentum of light1, 2, and it plays a crucial role in a variety of physical systems3, 4, 5, 6. It is usually assumed that both the optical momentum and the radiation-pressure force are naturally aligned with the propagation direction of light, given by its wavevector. Here we report the direct observation of an extraordinary optical momentum and force directed perpendicular to the wavevector, and proportional to the optical spin (degree of circular polarization). Such an optical force was recently predicted for evanescent waves7 and other structured fields8. It can be associated with the 'spin-momentum' part of the Poynting vector, introduced by Belinfante in field theory 75 years ago9, 10, 11. We measure this unusual transverse momentum using a femtonewton-resolution nano-cantilever immersed in an evanescent optical field above the total internal reflecting glass surface. Furthermore, the measured transverse force exhibits another polarization-dependent contribution determined by the imaginary part of the complex Poynting vector. By revealing new types of optical forces in structured fields, our findings revisit fundamental momentum properties of light and enrich optomechanics.