We use optical spectroscopy to investigate the electron-phonon interaction in Sr2IrO4, a well-known 5d transition metal oxide with spin-orbit entangled states. The temperature evolution in the optical spectra is well described by the Frohlich polaron model, indicating a large electron-phonon interaction. We further find that electrons in different orbitals selectively couple with different phonon modes. While J(eff) = 3/2 holes do not seem to couple with any phonons, J(eff) = 1/2 and 3z(2)-r(2) electrons mainly couple with in-plane and out-of-plane Ir-O bending modes, respectively. The symmetries of the orbitals and phonons are consistent with our observations.