Electrospun fibers for tissue engineering have recently seen significant advancements. In this study, we created composite fibers by combining Pistacia atlantica Gum-Resin and Poly(ε-caprolactone) (PCL) polymer using the electrospinning method. We examined the morphology, biodegradability, thermal stability, and hydrophilicity of the prepared scaffolds using Fourier transform infrared spectroscopy (FT-IR), scanning electron microscopy (SEM), thermogravimetric (TG) differential scanning calorimetry (DSC), and water contact angle measurements. The results indicated complete integration between the materials and successful synthesis of fibers through the electrospinning method. SEM images demonstrated bead-free fibers with different blending ratios of Gum-Resin and PCL. Fibers with a diameter of 100–200 nm and 1–7 μm were obtained with a 9:1 blending ratio of PCL to Gum-Resin. Additionally, PCL/Gum-Resin fibers with an 8:2 blending ratio exhibited an interwoven and porous fiber network structure with a 1–7 μm fiber diameter. The water contact angle measurements revealed the hydrophilic surface of the fibers, with a WCA of 61.2◦. Thermogravimetric (TG) and differential scanning calorimetric (DSC) analysis showed a melting peak at approximately 57◦. Cell culture results indicated good cytocompatibility of the fibers. The scaffold sample exhibited inhibitory activity against S. aureus (22 ± 0.26 mm) and E. coli (16.8 ± 0.15 mm) bacteria. These findings suggest that the fabricated fibers could serve as an effective scaffold for wound healing.