Context. The detection and characterization of exorings (rings around exoplanets) will help us to better understand the origin and evolution of planetary rings in the Solar System and beyond. However, exorings are still elusive, and new and clever methods for identifying them need to be developed and tested. Aims. We explore the potential of polarimetry as a tool for discovering and characterizing exorings. Methods. For this purpose, we improved the general publicly available photometric code Pryngles by adding the results of radiative transfer calculations with an adding-doubling algorithm that fully includes polarization. With this improved code, we computed the total and polarized fluxes and the degree of polarization of model gas giant planets with or without rings. Additionally, we demonstrate the versatility of our code by predicting the polarimetric signal of the puffed-up planet HIP 41378 f as if it had an exoring. Results. Spatially unresolved dusty rings can significantly modify the flux and polarization signals of the light that is reflected by a gas giant exoplanet along its orbit. Rings are expected to have a low polarization signal, but they will decrease the degree of polarization of reflected light when they cast a shadow on the planet and/or block part of the planet. The most diagnostic feature of a ring occurs around the ring-plane crossings when sharp changes in the flux and degree of polarization curves are predicted by our model. When we applied our methods to HIP 41378 f, we found that if it is surrounded by a ring, noticeable changes in the degree of polarization of reflected light will arise. Although the reflected light on the planet cannot yet be directly imaged, the addition of polarimetry to future observations would aid in the characterization of the system.