In this paper, we extend the concept of a matrix angular central Gaussian (MACG) distribution to the complex domain. First, we consider a normally distributed random complex matrix (Z) and demonstrate that its orientation exhibits a complex MACG (CMACG) distribution. We then discuss the distribution of the orientation of the linear transformation of the random matrix, the orientation of which has a CMACG distribution. Finally, we examine the family of distributions that leads to the CMACG distribution.