The two-dimensional (2D) Ruddlesden-Popper organic-inorganic halide perovskites such as (2D)-phenethylammonium lead iodide (2D-PEPI) have layered structure that resembles multiple quantum wells (MQW). The heavy atoms in 2D-PEPI contribute a large spin-orbit coupling that influences the electronic band structure. Upon breaking the inversion symmetry, a spin splitting ('Rashba splitting') occurs in the electronic bands. We have studied the spin splitting in 2D-PEPI single crystals using the circular photogalvanic effect (CPGE). We confirm the existence of Rashba splitting at the electronic band extrema of 35±10 meV, and identify the main inversion symmetry breaking direction perpendicular to the MQW planes. The CPGE action spectrum above the bandgap reveals spin-polarized photocurrent generated by ultrafast relaxation of excited photocarriers separated in momentum space. Whereas the helicity dependent photocurrent with below-gap excitation is due to spin-galvanic effect of the ionized spin-polarized excitons, where spin polarization occurs in the spin-split bands due to asymmetric spin-flip.