What do you exactly mean by this? Yes robots can phyiscally destroy humanity, under the control of someone, or something, whether it be a self improving algorithm or a physical being. The capabilities of power we can create have surpassed the grasps of human control, and so we have started (long ago) creating things that we can no longer put up a fight against.
But in theory channeling the question back and analysing it, robots cannot destroy humanity, because robots alone are just metal sculptures, incapable of anything without interruption from a living being, who then creates the unimaginably difficult string of code that would get a robot to 'destroy humanity'
But what is there to say they are not already, a robot is a a machine capable of carrying out a complex series of actions automatically, yes? So in effect, these self targeting missiles are robots, are they not, and they are destorying humanity, at whatever a scale. So does this answer your question? Yes? They already are?