A starting clutch control system applied to a vehicle in which an engine torque is inputted to a torque converter having a pump impeller and a turbine, and outputted to driving wheels through a clutch. the control system is configured to stop the engine while disengaging the clutch upon satisfaction of a predetermined condition when the vehicle is running, and to restart the stopping engine while engaging the clutch upon satisfaction of a predetermined restarting condition. According to the present invention, the control system is configured: to estimate a turbine torque of the torque converter based on an engine speed, and a capacity coefficient and a torque ratio of the torque converter, when the engine is required to increase a power to be restarted; to increase a torque transmitting capacity of the clutch in accordance with the estimated turbine torque; to estimate the turbine torque based on an air intake of the engine and an engine speed after a completion of an engagement of the clutch; and to control the torque transmitting capacity of the clutch in accordance with the estimated turbine torque.