The strong spin-orbit interaction in the organic-inorganic perovskites tied to the incorporation of heavy elements (textit{e.g.} Pb, I) makes these materials interesting for applications in spintronics. Due to a lack of inversion symmetry associated with distortions of the metal-halide octahedra, the Rashba effect (used textit{e.g.} 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, supported by the recent observation of a near record Rashba spin splitting in CH$_3$NH$_3$PbBr$_3$ using angle-resolved photoemission spectroscopy (ARPES). More experimental studies are needed to confirm and quantify the presence 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)$_2$MAPb$_2$I$_7$; BA = CH$_3$(CH$_2$)$_3$NH$_3$, MA = CH$_3$NH$_3$]. Our findings confirm the presence of a Rashba spin splitting via the dominance of precessional spin relaxation induced by the Rashba effective magnetic field. 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.
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