A new class of partially coherent sources that can produce stable rotating anisotropic rectangular hollow Gaussian array profiles in the far field is presented. The cross-spectral density function and the spectral density of this kind of source on the propagation are derived, and its propagation characteristics, which are quite different from twisted Gaussian Schell-model beams, are discussed. The results show that each hollow lobe in the array tends to rotate around the axis during propagation. In addition, the dimension of the array, the distance between the lobes of the array, and the number of rows and columns of the rectangular array can be flexibly manipulated by adjusting the source parameters. Our work may provide a method to generate rotating anisotropic array beams with hollow lobes, which could have certain reference values in optical manipulation.