The energy demands of the world have been accelerating drastically because of the technological development, population growth and changing in living conditions for a couple of decades. A number of different techniques, such as batteries and capacitors, were developed in the past to meet the demands, but the gap, especially in energy storage, has been increasing substantially. Among the other energy storage devices, supercapacitors have been advancing rapidly to fill the gap between conventional capacitors and rechargeable batteries. In this study, natural resources such as pistachio and acorn shells were used to produce the activated carbons for electrode applications in a supercapacitor (or an electrical double-layer capacitor—EDLC). The activated carbon was synthesized at two different temperatures of 700 °C and 900 °C to study its effect on porosity and performance in the supercapacitor. The morphology of the activated carbon was studied using scanning electron microscopy (SEM). A solution of tetraethylammonium tetrafluoroborate (TEABF4)/propylene carbonate (PC) was prepared to utilize in supercapacitor manufacturing. The performance of the EDLC was investigated using cyclic voltammetry (CV) and electrochemical impedance spectroscopy. Activated carbons from both the pistachio and acorn shells synthesized at 700 °C in argon gas for two hours exhibited better surface textures and porosity. There activated carbons also exhibited more capacitor-like behavior and lower real impedances, indicating that they would have superior performance compared to the activated carbons obtained at 900 °C. This study may be used to integrate some of natural resources into high-tech energy storage applications for sustainable developments.