We investigate the centrifugally driven curvature drift instability to study how field lines twist close to the light cylinder surface of an AGN, through which the free motion of AGN winds can be monitored. By studying the dynamics of the relativistic MHD flow close to the light cylinder surface, we derive and solve analytically the dispersion relation of the instability by applying a single particle approach based on the centrifugal acceleration. Considering the typical values of AGN winds, it is shown that the timescale of the curvature drift instability is far less than the accretion process timescale, indicating that the present instability is very efficient and might strongly influence processes in AGN plasmas.