The posit number system is a promising substitute for the IEEE 754 floating point standard, providing both dynamic range and enhanced precision. However, the lack of dedicated methods for computing trigonometric functions has hindered the adoption of posits in several applications that require high-precision, such as signal processing, computer graphics, robotics, and kinematics. This paper addresses this gap by utilizing the CORDIC (COordinate Rotational DIgital Computer) algorithm, an iterative method for approximating trigonometric functions. In this paper, existing CORDIC optimizations have been evaluated for their accuracy when applied to the posit number system. Building on these optimizations, this work introduces a rotation mode CORDIC algorithm tailored for posits. The proposed algorithm demonstrates significant improvements in speed and accuracy, achieving an accuracy improvement of 53% while reducing the iteration count by 76% when compared to a standard implementation.