Circular statistics has been applied to several areas of knowledge in which the input data is circular. Noisy measurements are still a problem in circular data applications and, like non-circular data, second-order statistics have some limitations to deal with non- Gaussian noise. Recently, a similarity function called correntropy has been successfully employed in applications involving impulsive noise for being capable of extracting more information than second-order methods. However, correntropy has not been studied from the perspective of circular data so far. This thesis defines a novel statistical measure called circular correntropy (CC). It uses the von Mises density function in order to redefine correntropy in this domain. In particular, it is proved analytically that the CC contains information regarding second-order and higher-order moments, being a generalization of the circular correlation measure. Its properties are studied as well as a new recursive solution for the Maximum Circular Correntropy Criterion (MCCC). The performance of this new similarity measure is evaluated as a cost function in nonlinear regression and time series prediction problems, where signals are contaminated with additive impulsive noise. Simulations demonstrate that CC is more robust than second-order circular statistics in impulsive noise environments.