Assuming that high-energy effects may alter the standard dispersion relations governing quantized fields, the influence of such modifications on various phenomena has been studied extensively in the literature. In different contexts, it has generally been found that, while superluminal dispersion relations hardly affect the standard results, subluminal relations can lead to (even substantial) modifications to the conventional results. A polymer quantized scalar field is characterized by a series of modified dispersion relations along with suitable changes to the standard measure of the density of modes. Amongst the modified dispersion relations, one finds that the lowest in the series can behave subluminally over a small domain in wave numbers. In this work, we study the response of a uniformly rotating Unruh-DeWitt detector that is coupled to a polymer quantized scalar field. While certain subluminal dispersion relations can alter the response of the rotating detector considerably, in the case of polymer quantization, due to the specific nature of the dispersion relations, the modification to the transition probability rate of the detector does not prove to be substantial. We discuss the wider implications of the result. © 2017 American Physical Society.