Immersed boundary methods provide a computational technique developed for simulation in fluid-structure interaction (FSI) problems with moving bodies using fixed grids, eliminating the need for dynamic mesh reconstruction. This significantly reduces computational costs while maintaining accuracy, making immersed boundary methods particularly valuable in applications such as biomechanics, fluid dynamics, and industrial aerohydrodynamics. Among these methods, the LS-STAG approach stands out for its efficiency and precision. To enhance numerical stability, it employs rectangular staggered grids, where velocity and pressure variables are sampled at different spatial locations. In two-dimensional scenarios, the method utilizes a 5-point discretization stencil. This makes it possible to use efficient solvers for systems of linear algebraic equations and parallelize computations. The LS-STAG method has been extended to various fluid types, including non-Newtonian fluids, which exhibit nonlinear stress-strain relationships. This paper focuses on power-law fluids, a subclass of viscous non-Newtonian fluids characterized by strain rate-dependent viscosity. To validate the LS-STAG-based numerical method implemented in the author’s in-house code, a benchmark test involving power-law fluid flow around a rotating circular cylinder is performed. The results for velocity profiles and drag coefficients show good agreement with known data. This consistency confirms the robustness of the developed solver in handling non-Newtonian flows with moving boundaries. The work underscores the adaptability of the LS-STAG method for complex rheological studies.