In this work, we developed simple polymer-based memristive devices specifically designed for biosensing applications. The devices consist of two gold electrodes connected by a biocompatible polymeric resistive layer made of poly(3,4 ethyldioxythiophene)poly(styrenesulfunate) (PEDOT:PSS) and poly(vinyl alcohol) (PVA). Device characterization was conducted under electrolyte conditions to fully mimic biological environments, a factor of crucial importance for effective biosensing. In particular, cyclic voltammetry (CV) was employed to electrochemically analyse the spray-coated resistive layer, whereas current-voltage (I-V) characteristic was used to demonstrate a capacitive-coupled memristive behavior characterized by non-pinched loop hysteresis. The memristive devices were subsequently functionalized with DNA aptamers to successfully detect histamine in the range of 0.03 to 230 μM. Our thin-film organic memristive devices show promise as cost-effective building blocks for memristive biosensing applications.