We experimentally demonstrate a RF-assisted four-state continuous-variable quantum key distribution (CV-QKD) system in the presence of turbulence. The atmospheric turbulence channel is emulated by two spatial light modulators (SLMs) on which two randomly generated azimuthal phase patterns are recorded yielding Andrews' azimuthal phase spectrum. Frequency and phase locking are not required in our system thanks to the proposed digital phase noise cancellation (PNC) stage. Besides, the transmittance fluctuation can be monitored accurately by the DC level in this PNC stage, which is free of post-processing noise. The mean excess noise is measured to be 0.014, and the maximum secret key rate of >20Mbit/s can be obtained with the transmittance of 0.85, while employing the commercial PIN photodetectors.