We demonstrate power-dependent steering of self-confined light beams propagating in the nonparaxial regime in a guest-host nonlinear medium. Exploiting the Janossy enhancement in dye-doped liquid crystals with reorientational response, we observe sub-mW spatial soliton self-steering as large as 39 degrees, accompanied by trapping of the light spontaneously emitted by the excited dye. The self-turning is modeled in terms of an effective transverse force stemming from the longitudinal electric field in the tightly confined beams, with good agreement between data and simulations.