The alignment of the wind turbine yaw to the wind direction is an important topic for wind turbine technology by several points of view. For example, the negative impact on power production of an undesired non-optimal yaw alignment can be impressive. The diagnosis of zero-point shifting of the yaw angle is commonly performed by adopting supplementary measurement sources, as for example, light detection and ranging (LIDAR) anemometers. The drawback is that these measurement campaigns have a certain cost against an uncertain diagnosis outcome. There is therefore an increasing interest from wind turbine practitioners in the formulation of zero-point yaw angle shift diagnosis techniques through the use of nacelle anemometer data. This work is devoted to this task and is organized as a test case discussion: a wind farm featuring six multi-megawatt wind turbines is considered. The study of the power factor Cp as function of the yaw error (estimated through nacelle anemometer data) is addressed. The proposed method has been validated through the detection of a 8 deg zero-point shift of the yaw angle of one wind turbine in the test case wind farm. After the correction of this offset, the performance of the wind turbine of interest is shown to be comparable with the nominal. The results of this work therefore support that an appropriate analysis of nacelle anemometer and operation data can be effective for the diagnosis of zero-point shift of the yaw angle of wind turbines.