Fundamental properties of the spin-noise signal formation in a quantum-dot microcavity are studied by measuring the angular characteristics of the scattered light intensity. A distributed Bragg reflector microcavity was used to enhance the light-matter interaction with an ensemble of n-doped (In,Ga)As/GaAs quantum dots, which allowed us to study subtle effects of coherent scattering at the quantum dot ensemble. Detecting the scattered light outside of the aperture of the transmitted light, we measured the basic electron spin properties, such as g factor and spin dephasing time. Further, we investigated the influence of the microcavity on the scattering distribution and possibilities of signal amplification by additional resonant excitation.