A statistical backscatter channel model for indoor clutter is developed for indoor RF sensing applications based on measurements. A narrowband 28 GHz sounder used a quazi-monostatic radar arrangement with an omnidirectional transmit antenna illuminating an indoor scene and a spinning horn receive antenna less than 1 m away collecting backscattered power as a function of azimuth. Median average backscatter power was found to vary over a 12 dB range, with average power generally decreasing with increasing room size. A deterministic model of average backscattered power dependent on distance to nearest wall and wall reflection coefficient reproduces observations with 4.0 dB RMS error. Distribution of power variation in azimuth around this average is reproduced within 1 dB by a random azimuth spectrum with a lognormal amplitude distribution and uniformly random phase. The model is extended to provide power distribution over both azimuth and delay (conveying range to scatterer) by combining azimuthal distribution with published results on power delay profiles in reverberant environments. The statistical model does not require a detailed room layout description, aiming to reproduce backscatter clutter statistics, as opposed to a deterministic response.