K₃ picene is a superconducting molecular crystal with a critical temperature of T_c = 7 or 18 K, depending on the preparation conditions. Using density functional theory we show that electron-phonon interaction accounts for T_c 3-8 K. The average electron-phonon coupling, calculated by including the phonon energy scale in the electron-phonon scattering, is λ = 0.73 and ω_log = 18.0 meV. Intercalant and intermolecular phonon modes contribute substantially (40 per cent) to λ as also shown by the isotope exponents of potassium (0.19) and carbon (0.31). The relevance of these modes makes superconductivity in K-doped picene peculiar and different from that of fullerenes.