Deep learning models for Natural Language Processing (NLP) tasks, such as Part-of-Speech (POS) tagging, usually have significant parameter counts that make them costly to train and deploy. Quantum Machine Learning (QML) offers a potential approach for building more parameter-efficient models. This paper proposes a hybrid quantum-classical gated recurrent unit model for POS tagging in code-mixed social media text. By integrating a quantum layer into the recurrent framework, our model achieved an accuracy comparable to the baseline classical model, while needing fewer parameters. Although the cut-off point in the parameters is modest in our setup, the approach is promising when scaled to deeper architectures. These results suggest that hybrid models can offer a resource-efficient alternative for NLP tasks.