I'd like to rotate 2 of my 23 inch screens, but neither of them have holes on the back for mounting. Does anyone know of a solution that will allow me to rotate these, such as an adjustable arm that clamps around the sides of the monitor to hold it up? Can't seem to find anything like that out there.
That doesn't really exist. You'd have to DIY something.
Or sell your current monitors, and buy 2 with VESA mounts.
What make/model do you have now?