Circular (angular) random variables, such as the angle of arrival(AOA) in direction finding systems and the phase error in digital phase-locked loops and digital phase interferometers, are best modeled by the von Mises distribution, not the ubiquitous Gaussian distribution. However, the Gaussian distribution has been commonly preferred in the performance analysis of AOA geolocation systems, mostly due to its mathematical tractability. This paper demonstrates the use of the von Mises distribution to model AOA measurement errors in direction finding systems and derives simple expressions for the Fisher information matrix (FIM) and the Cramer-Rao lower bound for the average miss distance. These results show that the use of the von Mises model in the performance analysis of AOA geolocation systems is entirely practicable.