The effects of plasma turbulence on the Compton scattering process are investigated in turbulent plasmas by the scattering of electromagnetic waves.  The Compton scattering cross section in astrophysical turbulent plasmas is obtained by the fluctuation-dissipation theorem and plasma dielectric function as a function of the diffusion coefficient, wave number, and Debye length.  It is demonstrated that the turbulence effect suppresses the Compton scattering cross section.  It is also shown that the turbulence effect on the Compton scattering process decreases with increasing thermal energy.  The dependence of the wave number on the total Compton scattering cross section including the Salpeter structure factor is also discussed.