Many microwave generators, especially high-power sources, utilize an azimuthally symmetric output mode such as the TM 01 circular waveguide or the coaxial TEM mode. If such a mode is projected into an antenna aperture and radiated directly, then a doughnut-shaped radiation pattern with a boresight null will result. Antenna designs to directly accommodate an azimuthally symmetric output mode and the high electric fields of high-power sources have been considered, but they tend to be low gain, do not radiate a boresight peak along the axis of the source, and the pattern peak direction changes with frequency. Mode conversion techniques to alter the aperture field distribution (i.e., TM 01 to TE 11 in circular waveguide) have also been explored, but losses and weight, size and cost additions impact negatively on total system design. This paper describes a novel antenna we call the coaxial beam-rotating antenna (COBRA) that mitigates many of the problems normally associated with the azimuthally symmetric output modes of high-power microwave sources. The COBRA accepts directly (without the need for mode conversion) an azimuthally symmetric guided mode of a microwave source and radiates a high-gain pattern with a boresight peak. In addition, the COBRA operates with a wide bandwidth, is compatible with the intense electric fields associated with high-power microwave sources, and the geometry of the antenna can be easily configured to produce an arbitrarily (elliptically) polarized boresight field. This paper presents the fundamental theory of operation, derives pertinent design and performance equations, and gives the measured operating characteristics of a COBRA prototype.