Electron-phonon coupling is at the core of various regimes of material-based science and technology. Taking 3C-silicon carbide (3C-SiC) as an example, despite its very wide application in high temperature and high power devices, the transport properties of 3C-SiC are not yet fully understood at the microscopic level because of inadequate knowledge in electron-phonon coupling. In this work, with electron-phonon coupling matrix elements calculated from first principles, the phonon limited carrier mobility of 3C-SiC is quantified by solving the Boltzmann transport equation. The calculated mobilities for both holes and electrons are in reasonable agreement with the experimental data. Unlike other polar semiconductors such as GaAs, where the polar-longitudinal-optical-phonon interactions are the dominant scattering mechanism, the mobilities of electrons and holes are dominated by the intravalley longitudinal acoustic (LA) phonon scattering at 300K due to the low occupation number of high-frequency polar longitudinal optical (LO) phonons in 3C-SiC. The dominant scattering mechanism in 3C-SiC varies with temperature. At high temperature (800K), LO phonons govern the scattering instead. The maximum mean free paths of electrons and holes at room temperature are found to be 40 nm and 15 nm, respectively.