In free-space optical communication, the propagation of a laser beam through the atmosphere causes wavefront distortions that decrease the coupling efficiency (CE) from free space to single-mode fiber. This tremendously degrades the performance of the communication channel even in the case of weak turbulence regime. In this Letter, we demonstrate that a multi-actuator adaptive lens working in closed loop with a wavefront sensor can strongly reduce the effect of turbulence while reducing the system complexity with respect to correction systems using deformable mirrors or liquid crystal spatial light modulators. We obtain a three-fold increase in the CE in weak turbulence regime.