Each wire rope construction will have an inherent torque characteristic where both ends of the rope are secured and an applied force will generate torque at the fixing points. Each wire rope construction will have an inherent turn characteristic where one end of the rope is free to rotate and an applied force will cause the free end of the rope to turn.
The torque or turn generated will depend upon the magnitude of the force applied and also upon the construction of the wire rope selected.In terms of resistance to rotation wire ropes can be divided into three basic catgories.

Single layer ropes have a much greater tendency to rotate under load than the two or three layer ropes which are often referred to as rotation resistant. Similarly the three layer rope will have less tendency to rotate when compared with the two layer rope.
Both the two layer and three layer ropes depend on torsional balance between the outer and inner layers to create rotational stability. With correct rope selection rotation should not cause a problem in service provided that the rope has been correctly balanced in design and manufacture.
Before selecting a rotation resistant rope, consideration should be given to a single layer construction. If the application/duty in question does not require the rope to resist rotation then it is possible that a single layer rope can represent a more robust and more effective solution.
Safety note - Single layer Langs lay ropes (where the direction of strand lay is the same as the direction of rope lay) have exceptionally bad rotational characteristics and must only be used in applications where both ends of the rope are securely fixed.