A firearm accessory mount can be used to mount an aiming device to a firearm. The accessory mount can include a base plate having a top and bottom side. A first scope mounting ring and a second scope mounting ring can be coupled to the base plate and separated a distance from each other. Each of the scope mounting rings can be coupled to different portions of an aiming device, such as a rifle scope. A threaded aperture can extend through the base plate and can be positioned between the scope mounting rings. A leveling screw can be inserted in the aperture and have a substantially flat top surface that extends above the top side of the base plate. When coupled to the accessory mount, a portion of the aiming device can contact the top surface of the leveling screw to level the aiming device.