Originally designed for wind velocity estimation over the ocean, scatterometers have been applied to weather forecasting, global climatological studies, and monitoring of large-scale human interaction on the planet. Launched in September of 2009, the Oceansat-2 Ku-band scatterometer (OSCAT) is an excellent candidate for continuing the data time series begun with QuikSCAT, which was the SeaWinds scatterometer flown on the QuikSCAT mission 1999-2009. Some processing algorithms require knowledge of the spatial response function (SRF) of the scatterometer. With limited knowledge of OSCAT implementation, and thus its SRF, a procedure is developed for estimating the SRF. The estimation procedure uses scatterometer measurements over islands to invert the radar equation. A mathematical model is developed that reduces the solution to rank-reduced least-squares estimation. The geographic sampling region is discussed, and a simulation is performed to verify the efficacy of the method, while also providing guidelines for island choice and the number of singular values used in rank reduction. The utility of OSCAT SRF estimates is demonstrated through the construction of an enhanced-resolution radar backscatter image over the Amazon rainforest.