If you are ready to use the turret, simply right click your mouse button, but make sure you have pressed R to reload it first. You will need to have crafted some ammo and then press R while holding the Junk Turret to make sure it’s loaded, once loaded, use it as if it were any other gun.
Unless you happened to have it in your active Hotbar, you may not have thought to try using it as a weapon, but believe it or not, the turret can be picked up and manually fired.
