The spin-orbit interaction (SOI) plays an essential role in materials properties, and controlling its intensity has great potential in the design of materials. In this work, asymmetric [(La0.7Sr0.3MnO3)8/(BaTiO3)t/(SrTiO3)2]8 superlattices were fabricated on (001) SrTiO3 substrate with SrO or TiO2 termination, labelled as SrO-SL and TiO2-SL, respectively. The in-plane angular magnetoresistance of the superlattices shows a combination of two- and four-fold symmetry components. The coefficient of two-fold symmetry component has opposite sign with current I along [100] and [110] directions for TiO2-SL, while it has the same sign for SrO-SL. Detailed study shows that the asymmetric cation inter-mixing and ferroelectricity-modulated electronic charge transfer induce asymmetric electronic potential for SrO-SL with dominating Rashba SOI, and symmetric electronic potential for TiO2-SL with dominating Dresselhaus SOI induced by BaTiO3. This work shows that the Rashba and Dresselhaus SOIs are sensitive to the ferroelectric polarization in the asymmetric structure.