This paper presents a design of a horizontally polarized antenna array for a new DLR airborne Ka band synthetic aperture radar system with the maximum gain of 24 dB, low cross-pol level of 40 dB and a shaped radiation pattern with low sidelobe level in both azimuth and elevation planes below -18 dB. It has been designed using the slotted waveguide antenna (SWA) technology for the center frequency equal to 35.5 GHz. The transverse slots have been cut into the narrow waveguide wall and the use of iris pairs placed inside enable the radiation. A suitable feeding network consisting of a conventionally H-plane T junction power divider and a directional waveguide coupler has been also described. Based on theoretical principles, the antenna array as well as the corresponding power splitter have been developed and fabricated while meeting mechanical and electrical system demands. The measurement results of the manufactured prototype have been presented and a good agreement with requirements has been achieved.