The outstanding photovoltaic performance in hybrid organic-inorganic perovskites (HOIPs) relies on their desirable carrier transport properties. In the HOIPs, strong spin-orbit coupling (SOC) and structural inversion asymmetry give rise to a giant spin splitting in the conduction and valence bands, that is, the Rashba effect (RE), a subject intensively studied in spintronics. Here we show that this giant RE can manifest itself in charge transport and is the key to understanding carrier mobility and its temperature dependence in the HOIPs. The RE greatly enhances acoustic-phonon scattering (APS) and alters the temperature dependence of carrier mobility from T(-3/2) to T(-1). Meanwhile, it reduces polar-optical phonon scattering (POPS). In CH3NH3PbI3, the carrier mobility is limited by the APS for temperatures up to 100 K, above which the POPS becomes dominant. The effective polar coupling is moderate, α = 1.1, indicating that band conduction is still a valid description of charge transport. Our results account for the observed carrier transport behaviors over the entire temperature range and highlight the importance of SOC in charge transport in the HOIPs.