Biocompatible polymer-based scaffolds hold great promise for neural repair, especially when they are coupled with electrostimulation to induce neural differentiation. In this study, a combination of polyacrylonitrile/polyaniline (PAN/PANI) and Carbon Nanotubes (CNTs) were used to fabricate three different biomimetic electrospun scaffolds (samples 1, 2 and 3 containing 0.26 wt%, 1 wt% and 2 wt% of CNTs, respectively). These scaffolds underwent thorough characterization for assessing electroconductivity, tensile strength, wettability, degradability, swelling, XRD, and FTIR data. Notably, scanning electron microscopy (SEM) images revealed a three-dimensional scaffold morphology with aligned fibers ranging from 60 nm to 292 nm in diameter. To comprehensively investigate the impact of electrical stimulation on the nervous differentiation of the stem cells seeded on these scaffolds, cell morphology and adhesion were assessed based on SEM images. Additionally, scaffold biocompatibility was studied through MTT assay. Importantly, Real-Time PCR results indicated the expression of neural markers—Nestin, β-tubulin III, and MAP2—by the cells cultured on these samples. In comparison with the control group, samples 1 and 2 exhibited significant increases in Nestin marker expression, indicating early stages of neuronal differentiation, while β-tubulin III expression was significantly reduced and MAP2 expression remained statistically unchanged. In contrast, sample 3 did not display a statistically significant upturn in Nestin maker expression, while showcasing remarkable increases in the expression of both MAP2 and β-tubulin III, as markers of the end stages of differentiation, leading to postmitotic neurons. These results could be attributed to the higher electroconductivity of S3 compared to other samples. Our findings highlight the biomimetic potential of the prepared scaffolds for neural repair, illustrating their effectiveness in guiding stem cell differentiation toward a neural lineage.