Originally the German word "Draht" signified a twisted thread. In Middle High German the term came to be used as well for metal wires which were drawn - rather than twisted - by "Drahtzieher" (wire drawers).
Marionettes were moved by drawing on the wires on which they were suspended. In the 18th century the word "Drahtzieher" was used to denote any person "drawing the wires" in the background, similar to the English "pulling strings".
See Also
Adapted from “"We do it straight" — Wire Straightening”, p. 201 (ISBN 3-00-005897-4).