Worldwide, human health is affected by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Hence, the fabrication of the biosensors to diagnose SARS-CoV-2 is critical. In this paper, we report an electrochemical impedance spectroscopy (EIS)-based aptasensor for the determination of the SARS-CoV-2 receptor-binding domain (SARS-CoV-2-RBD). For this purpose, the carbon nanofibers (CNFs) were first decorated with gold nanoparticles (AuNPs). Then, the surface of the carbon-based screen-printed electrode (CSPE) was modified with the CNF-AuNP nanocomposite (CSPE/CNF-AuNP). After that, the thiol-terminal aptamer probe was immobilized on the surface of the CSPE/CNF-AuNP. The surface coverage of the aptamer was calculated to be 52.8 pmol·cm. The CSPE/CNF-AuNP/Aptamer was then used for the measurement of SARS-CoV-2-RBD by using the EIS method. The obtained results indicate that the signal had a linear-logarithmic relationship in the range of 0.01-64 nM with a limit of detection of 7.0 pM. The proposed aptasensor had a good selectivity to SARS-CoV-2-RBD in the presence of human serum albumin; human immunoglobulins G, A, and M, hemagglutinin, and neuraminidase. The analytical performance of the aptasensor was studied in human saliva samples. The present study indicates a practical application of the CSPE/CNF-AuNP/Aptamer for the determination of SARS-CoV-2-RBD in human saliva samples with high sensitivity and accuracy.