To bestow intelligent functions upon clothing textiles, wearable electronics must be able to accommodate complex deformations. Both stretchable and bendable building blocks have previously been demonstrated, but torsionable components are still lacking. Here we report a fiber-shaped flexible supercapacitor that is highly stable under torsional deformations, with a very small capacitance variation around its average value (<±2%) even under severe twisting. The torsionable supercapacitor is fabricated from shearable carbon nanotube films. When such a film is integrated with an elastic fiber as an electrode, it is capable of withstanding torsion levels up to 20 000 rad m⁻¹ with relatively stable conductivity. As a result, fiber-shaped supercapacitors fabricated from such torsionable electrodes can maintain an almost unchanged capacitance during twisting.