Evanescent electromagnetic fields near a waveguide can exert a transverse radiation force on scattering objects. To prove this experimentally, we demonstrate light-induced orbiting of isotropic, dielectric microparticles around an optical nanofiber that guides elliptically polarized, fundamental modes. The orbit frequency is proportional to the helicity of the coupled light. Interestingly, the observed motion is opposite to the energy flow circulation around the fiber. This result verifies the theoretically predicted negative optical torque on a sufficiently large particle in the vicinity of a nanofiber.