Silicon nanowires are reported for their application in bio sensing area and their potential in the detection of various biomolecules. In the present work, freestanding two-terminal Schottky-barrier silicon nanowire arrays exhibiting memristive behavior are fabricated to obtain Memristive-Biosensors. Scanning electron microscopy reveal details on the morphology of the fabricated structures. The memristive devices are functionalized with anti-free-Prostate Specific Antigen (PSA) antibody by two strategies: a) direct passive adsorption on the device surface, and b) bio-affinity approach using Biotin-Streptavidin combination. The electrical behavior of the so-obtained Memristive-Biosensors is examined dealing with the two systems of bio-functionalization. The presence of biomolecules linked to the surface of the nanostructures is detected by a voltage gap appearing in the memristive electrical characteristics. The system shows the potential for applications in molecular diagnostics especially due to possibilities for detection in the femto molar ranges that allow early detection of the cancer disease.