In the conventional spin noise spectroscopy, the probe laser light monitors fluctuations of the spin orientation of a paramagnet revealed as fluctuations of its gyrotropy, i.e., circular birefringence. For spins larger than 1/2, there exists spin arrangement of a higher order—the so-called spin alignment—which also exhibits spontaneous fluctuations. We show theoretically and experimentally that alignment fluctuations manifest themselves as the noise of the linear birefringence. In a magnetic field, the spin-alignment fluctuations, in contrast to those of spin orientation, show up as the noise of the probe-beam ellipticity at the double Larmor frequency, with the most efficient geometry of its observation being the Faraday configuration with the light propagating along the magnetic field. We have detected the spin-alignment noise in a cesium-vapor cell probed at the wavelength of D2 line (852.35 nm). The magnetic-field and polarization dependence of the ellipticity noise are in full agreement with the developed theory.