The effects of angle approximation and founding in the CORDIC processor have been intensively studied for the determination of design parameters. However, the conventional analyses provide only the error bound which results in large discrepancy between the analysis and the actual implementation. Moreover, some of the signal processing architectures require the specification in terms of the mean squared error (MSE) as in the design specification of FFT processor for OFDM. This paper proposes a fixed point MSE analysis based on the variance propagation for more accurate error expression of CORDIC processor. It is shown that the proposed analysis can also be applied to the modified CORDIC algorithms. As an example of application, an FFT processor for OFDM using the CORDIC processor is presented. The results show close match between the analysis and simulation.