Marine current turbine commercial prototypes have now been deployed and arrays of multiple turbines under design. The tidal flows in which they operate are highly turbulent, but the characteristics of the inflow turbulence have not being considered in present design methods. This work considers the effects of inflow turbulence on the wake behind an actuator disc representation of a marine current turbine. Different turbulence intensities and integral length scales were generated in a large eddy simulation using a gridInlet, which produces turbulence from a grid pattern on the inlet boundary. The results highlight the significance of turbulence on the wake profile, with a different flow regime occurring for the zero turbulence case. Increasing the turbulence intensity reduced the velocity deficit and shifted the maximum deficit closer to the turbine. Increasing the integral length scale increased the velocity deficit close to the turbine due to an increased production of turbulent energy. However, the wake recovery was increased due to the higher rate of turbulent mixing causing the wake to expand. The implication of this work is that marine current turbine arrays could be further optimized, increasing the energy yield of the array when the site-specific turbulence characteristics are considered.