The strong spin-orbit interaction in the organic-inorganic perovskites tied to the incorporation of heavy elements (e.g., Pb and I) makes these materials interesting for applications in spintronics. In conjunction with a lack of inversion symmetry associated with distortions of the metal-halide octahedra, surfaces and interfaces, or the application of a bias, the Rashba effect (used in spin field-effect transistors and spin filters) has been predicted to be much larger in these materials than in traditional III-V semiconductors such as GaAs. Evidence of strong Rashba coupling has been observed in both 3D (bulk) and 2D perovskites, with the relative role of bulk and surface Rashba contributions in the former case under active debate. The varying size of the reported spin splittings points to the need for more experimental studies of Rashba effects in the organic-inorganic perovskite family of materials. Here, we apply time-resolved circular dichroism techniques to the study of carrier spin dynamics in a 2D perovskite thin film [(BA)2MAPb2I7; BA = CH3(CH2)3NH3, MA = CH3NH3]. Our findings confirm the presence of a Rashba spin splitting via the dominance of precessional spin relaxation induced by the Rashba effective magnetic field (also known as D’yakonov Perel spin relaxation). The size of the Rashba spin splitting in our system was extracted from simulations of the measured spin dynamics incorporating LO-phonon and electron-electron scattering, yielding a value of 10 meV at an electron energy of 50 meV above the band gap, representing a 20 times larger value than in GaAs quantum wells.