Based on the angular spectrum theory of plane wave, the orbital angular momentum steer asymmetric splitting in photonic spin Hall effect (SHE) is studied. Taking the beam reflection at an air-glass interface for example, a propagation model describing the SHE of vortex beam is established, which clearly shows that the transverse displacements of left-handed and right-handed circular polarization components are asymmetric with regard to the incident plane. Particularly, the displacement magnitudes and directions of the two spin components are significantly affected by the topological charge of vortex beam. The asymmetric splitting is steered by orbital angular momentum which can be regarded as integral transverse shifts of two spin components for the incident plane. The integral transverse shifts correspond to Imbert-Fedorov effects of linear polarization vortex beam. The physics nature of these phenomenon are attributable to the spin-orbit interaction and orbit-orbit conversion at the interface, and this is little different from its symmetric counterpart for Gauss beams. The results suggest that the orbital angular momentum of light provides an alternative degree of freedom for tuning the photonic SHE.