The subject of this paper is the Antarctic Circumpolar Current (ACC) as the waveguide for Rossby waves. The ACC is the region where Rossby waves manifest differently in comparison to other parts of the World Ocean. The ACC is not only the waveguide for Rossby waves where wave kinetic energy is modified by jets, yet the region where Rossby waves interact with the flow. This manuscript contains a theoretical discussion of idealized Rossby wave dynamics and then computes a set of waveguide boundaries for the ACC, based on analysis of the propagation characteristics of sea surface height from satellite altimeter data. Since the linear theory of Rossby waves is not suitable within the waveguide areas, we propose a nonlinear approach that can explain the eastward propagation of Rossby waves in the ACC. We use the nonlinear theory of Rossby waves and zonal jets interaction, based on the fact that the nonlinearity in the long-wave approximation for Rossby waves exactly compensates the Doppler shift. The dispersion equation agrees well with altimetry data and provides a reasonable explanation to the propagation of the Rossby waves eastward within the ACC. We detect the northern and the southern waveguide boundaries for the ACC using altimetry and compare them to the climatological fronts in the ACC. We reveal that the Polar Front and the northern and southern branches of the Subantarctic Front are mostly located inside the waveguide in the South Ocean except the Indian sectors of the (30° to 90° E).