A rifle scope mount system includes a base having forward and rear mounting blocks attachable to a rifle barrel. Forward and rear scope clamp rings are attachable to a telescope engagable with the forward and rear mounting blocks, respectively, to mount the telescope to the gun. The forward mounting block has a female dovetail recess for rotatably receiving a male dovetail stud extending from the forward clamp ring. The rear mounting block has a flat upper surface. The rear clamp ring has a flat lower surface which is coplanar with the flat upper surface when the male dovetail stud and the female dovetail recess are mated. A first windage screw is threaded into a first hole in a first side of the rear mounting block so that its head extends above the flat upper surface and engages one side of the rear clamp ring. A second windage screw is threaded into a second hole on the opposite side of the rear mounting block. The head of the second windage screw has a flat surface. The second windage screw can be rotated so that its flat surface is co-planar with the upper flat surface, whereby the flat lower surface of the rear clamp ring can be slid along the flat upper surface. The first windage screw is then rotated so that its head tightly engages the second side of the pedestal of the rear clamp ring. A removable clip can be attached to engage the second windage screw within a coin slot therein to facilitate tightening and loosening of the second windage screw.