A spectral method for solving the steady flow of a shear-thinning Ellis fluid is discussed for the case of a planar channel with corrugated boundaries. Polynomial approximations are employed for the velocity and viscosity distributions in the regions around singularities. The proposed algorithm employs a fixed computational domain with the physical domain of interest submerged inside the computational domain. The flow boundary conditions are imposed using the concept of immersed boundary conditions. The method, thus, eliminates the need for grid generation. The algorithm relies on Fourier expansions in the flow direction and Chebyshev expansions in the transverse direction. Various tests confirm spectral accuracy of the algorithm.