We formulate the effective Hamiltonian of Rashba spin-orbit coupling (RSOC) in LaAlO SrTiO 3 3(LAO/STO) heterostructures. We derive analytical expressions of properties, e.g. Rashba parameter, effective mass, band edge energy and orbital occupancy, as functions of material and tunable heterostructure parameters. While linear RSOC is dominant around the Γ-point, cubic RSOC becomes significant at the higher-energy anti-crossing region. We find that linear RSOC stems from the structural inversion asymmetry (SIA), while the cubic term is induced by both SIA and bulk asymmetry. Furthermore, the SOC strength shows a striking dependence on the tunable heterostructure parameters such as STO thickness and the interfacial electric field which is ascribed to the quantum confinement effect near the LAO/STO interface. The calculated values of the linear and cubic RSOC are in agreement with previous experimental results.the SOC which accounts for the properties of the heterostructure, had been deliberately introduced, and the contribution of the bulk STO as well as the inter-orbital hopping was ignored. Significantly, the large spin splitting at the anti-crossing region, a signature of the multi-orbital effects, has not been fully elucidated.Recently, a theory based on k.p model [35, 36], including the contribution of the bulk STO, predicted a spin splitting induced by the inter-orbital hopping and interfacial band-bending. However, a complete picture of the multi-orbital Rashba SOC is still lacking. In this work, we aim to construct the effective Hamiltonian of Rashba spin-orbit coupling system in STObased structures, taking into account the underlying factors such as the confinement effect, as well as interface effects including inversion symmetry breaking (ISB) and band-bending. We derive analytical expressions of properties, e.g. Rashba parameter, effective mass, band edge energy and orbital occupancy, as functions of material and tunable heterostructure parameters. We show that the type and strength of spin-orbit coupling as well as the orbital selectivity are tunable by controlling geometric factor such as STO thickness and by applying electric field via gate voltage. The thickness and gate control of SOC provides a possible avenue for optimization of Rashba SOC for spintronics applications and devices.