RainCube, which stands for Radar in a CubeSat, is a technology demonstration mission to enable Ka-band precipitation radar technologies on a low-cost, quick-turnaround platform. The proposed mission is to develop, launch, and operate a 35.75 GHz radar payload on a 6U CubeSat. This mission will validate a new architecture for Ka-band radars and an ultra-compact deployable Ka-band antenna in a space environment. RainCube will also demonstrate the feasibility of a radar payload on a CubeSat platform. Numerical climate and weather models depend on measurements from space-borne satellites to complete model validation and improvements. Precipitation profiling capabilities are currently limited to a few instruments deployed in Low Earth Orbit (LEO), which cannot provide the temporal resolution necessary to observe the evolution of short time-scale weather phenomena and improve numerical weather prediction models. A constellation of precipitation profiling instruments in LEO would provide this essential capability, but the cost and timeframe of typical satellite platforms and instruments make this solution prohibitive. Thus, a new instrument architecture that is compatible with low-cost satellite platforms, such as CubeSats and SmallSats, will enable constellation missions and revolutionize climate science and weather forecasting. RainCube will design, build, and test a Ka-band radar payload that is compatible with a 6U CubeSat bus and current CubeSat capabilities. The integrated CubeSat will be launched and operated from LEO, and post-processing of the on-orbit data will be used to validate the functional operation and performance of the radar payload. The proposed mission will increase the technology readiness of the Ka-band radar architecture and antenna from an entry TRL 4-5 to an exit TRL 7 in a period of performance of two years and two months.