We report here on anisotropy of spin polarization obtained in lateral all-semiconductor, all-electrical spin injection devices employing p+-(Ga,Mn)As/n+-GaAs Esaki diode structures as spin aligning contacts, resulting from the dependence of the efficiency of spin tunneling on the orientation of spins with respect to different crystallographic directions. We observed an in-plane anisotropy of 8% in the case of spins oriented either along [1[overline 1]0] or [110] direction and 25% anisotropy between in-plane and perpendicular-to-plane orientations of spins.