Time-resolved x-ray magnetic circular dichroism (XMCD) enables a unique spectroscopic view on complex spin and charge dynamics in multi-elemental magnetic materials. So far, its application in the soft-x-ray range has been limited to synchrotron-radiation sources and free-electron lasers. By combining a laser-driven plasma source with a magnetic thin-film polarizer, we generate up to 30% circular polarization in the soft-x-ray regime, enabling the first XMCD spectroscopy at the Fe $L$ edges in a laser laboratory, to our knowledge. Our approach can be readily adapted to other transition metal $L$ and rare earth $M$ absorption edges, and with a temporal resolution of $\lt 10\;{\rm ps}$, a wide range of ultrafast magnetization studies can be realized.