Variable-stiffness artificial muscles are important in many applications including running and hopping robots, human-robot interaction and active suspension systems. Previously used technologies include pneumatic muscles, layer and granular jamming, series elastic actuators, and shape memory polymers. All of these are limited in terms of cost, complexity, the need for fluid power supplies, or controllability. In this article, we present a new concept for variable-stiffness artificial muscles (the twisted rubber artificial muscle, TRAM) made from twisted rubber cord which overcomes these limitations. Rubber cord is inexpensive, readily available, and inherently compliant. When an extended piece of rubber cord is twisted, the tensile force it exerts is reduced and its stiffness is altered. This behaviour makes twisted rubber ideal for use as an artificial muscle, since its output force and natural stiffness are both controllable by varying twist angle. We investigate the behaviour of four types of rubber cord and evaluate which type of rubber allows for the greatest reversible reduction in average stiffness (fluoroelastomer (FKM standard) rubber, 56.42% reduction) and initial stiffness (silicone rubber, 92.62%). Tensile force and stiffness can be further altered by increasing the twist angle of the artificial muscle beyond a threshold angle, which initiates nonlinear buckling behaviour. This, however, can cause plastic deformation of the artificial muscle. Using a single TRAM, we show how the equilibrium position and natural frequency of a system can be simultaneously altered by controlling twist angle. We further demonstrate independent position and stiffness control of a functional robotic arm system using an antagonistic pair of TRAMs. TRAMs are ready for immediate inclusion in a wide range of robotic systems.