We have investigated the 3Heða; cÞ7Be radiative capture reaction using the pionless Effective Field Theory (EFT). The amplitude, cross-section, and S-factor for the E1 and E2 transitions to the 7Be ground state have been computed using the Faddeev equation approach up to Next-to Leading Order in the astrophysical energy range. Our aim has been the study of Coulomb interaction effects and the contribution of EFT higher-order calculations in optimizing the results. The computed S-factor for the reaction agrees with experimental data and previous theoretical calculations.