Generating a high quality vortex beam carrying orbital angular momentum (OAM) is of importance in the application of the OAM to target detections or communications. This paper presents a semi-blind method to calibrate the uniform circle array (UCA) OAM generating system by using a virtual receiving sensor array without knowing the precise position of this auxiliary array. A low computational complexity algorithm is proposed to solve the maximum likelihood estimate (MLE) for the amplitude and phase errors of the transducers of the UCA based on the separation of parameters to be estimated. Moreover, this MLE is proved to be related to the beamforming of the virtual array. Simulations indicate that this method can estimate the mismatch parameters of the UCA effectively, and experiments in an anechoic tank show that the OAM generating system can generate a desirable vortex beam after we compensate each transducer of the UCA.