In this study, using the results of a DNS of drag-reduced turbulent channel flow, vortical flow structures especially in the near-wall region are investigated. For this purpose, a Lagrangian Monte-Carlo method has been used to simulate the spatial orientation of fibers. Namely, the flow field is treated in an Eulerian manner whereas the fiber dynamics is described by a Lagrangian point of view. This method yields the exact solution of the governing equations. Vorticity fluctuations in the channel are studied and it turns out that the level of these fluctuations decreases in the drag-reduced flow. The reason for this reduction is explained using the reduction in velocity gradient fluctuations. Also, the distribution of the angle between the vorticity axis and the wall is studied and it turns out that horseshoe vortices exist in both flows. However, in the drag-reduced flow, they are formed farther away from the wall which indicates a weakening of sweep and ejection mechanism in the vicinity of the wall. This weakening leads to drag reduction. Also, the orientation of vortices in the drag-reduced flow is well ordered.