I've done rope like that in the past, it was quite straightforward.
Get hold of the appropriate gauge fine metal wire. Take a length of it and fold it into double. Secure it firmly in one end, then secure the other end onto some kind of twistable handle, then simply twist away whilst stretching the wire taut. Clip away either end with clippers when you are done and you should have a length of evenly twisted rope.
For acquiring wire, not sure what's your best bet here but florists could be an option. They should have thin wire for floral arrangements. My florist's wire has a green plastic coating that breaks when agitated too much, ideally you would get hold of bare metal wire to avoid this.
For securing the first end, use something sturdy (as you will be pulling at the other end). A vice would be great, or some thin bar that is otherwise firmly secure. Easiest way to secure it around a bar is just to put the middle of the wire up against it, fold around both halves and twist to fasten it.
For the twistable handle in the other end I would use something like a screwdriver, a sturdy ballpoint pen or a wooden dowel. You don't need industrial strength fixtures but it's good to have enough strength in the components to be able to keep the wire under tension as you twist, else the wire might want to coil up into s-shapes. If at first certain parts of the wire accumulate more twist than others, don't worry. As you keep twisting the less twisted parts should catch up.
As the wire twists up it reduces quite substantially in length so keep that in mind and use enough when you start. Perhaps do a little test first to get a feel for it.
Hope that works for ya! Should be an easy job once you get the hang of it and have the right tools.