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Graphene-like carbon fibres (GLCFs) have demonstrated their excellence for supercapacitors (SCs) due to their physical and structural properties. However, the complex synthesis routes for GLCFs hinder their widespread use in SCs. Therefore, we report a facile route for synthesizing high-quality GLCFs from waste cotton using a two-step synthesis approach. The synthesized GLCFs exhibited a high-quality graphitic skeleton, as evidenced by Raman analysis, with a 2D band indicative of a graphene-like structure. The FESEM images of GLCFs showed a well-established 3D network of folded graphene layers, making them suitable for faster charge-carrier transport in supercapacitor devices. To understand the electronic behaviour of these GLCFs for SC applications, we conducted a detailed density functional theory (DFT) investigation using the Synopsys-QuantumATK framework. As these GLCFs are supposed to consist of graphene nanosheets (GNSs), their structural, electrical, and capacitive properties were examined under bending conditions. The investigation showed that quantum capacitance reached a maximum under bending conditions, indicating that the bending of GNSs is the most favourable condition for attaining energy-storage properties. As GLCFs consist of bent sheets of GNSs, efficient charge-storage properties were expected, as confirmed by our experimental analysis. GLCFs showed a specific capacitance of 411.24 F g⁻¹ at a scan rate of 5 mV s⁻¹ in 1 M H₂SO₄ in a three-electrode set-up, with excellent capacitance retention over 5000 cycles. Further, we fabricated a GLCF-based coin cell (CR-2032) and achieved a maximum gravimetric capacitance of 31.79 F g⁻¹, maximum areal capacitance of 41.28 mF cm⁻², maximum energy density of 8.65 Wh kg⁻¹, and maximum power density of 105.00 W kg⁻¹, confirming its capacitive behavior and reasonable electrochemical performance as a symmetric supercapacitor.