The structure of the vorticity field in compressible mixing layers is studied using direct numerical simulations of temporally evolving mixing layers. The probability distribution of the inclination angles of the vorticity vectors with respect to various axes are analyzed. Spanwise projections of vorticity vectors have a tendency to align at angles -45° and 135° with respect to the streamwise direction. On streamwise and transverse planes, the projected vorticity vectors tend to align at very small angles with respect to the mean vorticity vector. These distributions are uninfluenced by changes in compressibility. Orientations of vortex filaments, which are dominant contributors to the vorticity covariances, are also identified. These orientations are independent of the transverse location within the turbulent core. The orientations of the projections of these filaments on to different planes are found out. Compressibility has no effect on the orientation of vorticity vectors contributing most to covariances. © 2019 IOP Publishing Ltd.