A hybrid conjugated polymer is presented that supports spike-timing-dependent plasticity (STDP) for neuromorphic computing devices while enabling environmental sustainability through biodegradability. The polymer, distinguished by its carbazole backbone and electrically responsive pendant carbazole groups, forms a two-terminal device that exhibits analog STDP behavior. Demonstrations focus on fundamental switching characteristics using individual devices, offering insights relevant to temporal learning tasks such as speech and image recognition. The energy cost per programming event is 60 nJ. Biodegradation is demonstrated using Pseudomonas resinovorans CA10 lysate, supporting reduced electronic waste. This work introduces a sustainable soft-matter platform for synaptic device development.