We study the effect of lower hybrid waves on edge turbulence using a set of two Langmuir probes inserted in the scrape-off layer of the Tore Supra tokamak. We use the cross-correlation coefficient to assess the interplay between turbulence and the LH waves. We found that turbulence is affected at high plasma current even at relatively low LH powers. When the plasma current is below 1 MA, this effect disappears. Finally, we show that the level of fluctuations and the cross-correlation amplitude are correlated whereas the increase of the first leads to the increase of the second. The role of the plasma current could reflect that the exchange of the RF waves with edge turbulence is occurring in the closed field lines rather in the open field lines range.