A rotating coupling system for a closing element, such as a door, window, door or the like, and a stationary support structure, such as a wall, floor, frame or the like includes a hinge device anchorable to the closing element and a mounting plate anchorable to the stationary support structure. The hinge device has a hinge body and a pivot defining a first axis, and are coupled each other to rotate one with respect to the other around the axis. In particular, the pivot includes a coupling portion, which protrudes from the hinge body, and the mounting plate includes a plate-shaped body having a seat that receives the coupling portion of the pivot. The plate-shaped body further includes an adjusting member to adjust its position with respect to the stationary support structure.