We present the first Faraday rotation measure (RM) grid study of an individual low-mass cluster -- the Fornax cluster -- which is presently undergoing a series of mergers. Exploiting commissioning data for the POlarisation Sky Survey of the Universe's Magnetism (POSSUM) covering a $\sim34$ square degree sky area using the Australian Square Kilometre Array Pathfinder (ASKAP), we achieve an RM grid density of $\sim25$ RMs per square degree from a 280 MHz band centred at 887 MHz, which is similar to expectations for forthcoming GHz-frequency all-sky surveys. We thereby probe the extended magnetoionic structure of the cluster in unprecedented detail. We find that the scatter in the Faraday RM of confirmed background sources is increased by $16.8\pm2.4$ rad m$^{-2}$ within 1 degree (360 kpc) projected distance to the cluster centre, which is 2--4 times more extended than the presently-detectable X-ray-emitting intracluster medium (ICM). The Faraday-active plasma is more massive than the X-ray-emitting ICM, with an average density that broadly matches expectations for the Warm-Hot Intergalactic Medium. The morphology of the Faraday depth enhancement exhibits the classic morphology of an astrophysical bow shock on the southwest side of the main Fornax cluster, and an extended, swept-back wake on the northeastern side. Our favoured explanation is an ongoing merger between the main cluster and a sub-cluster to the southwest. The shock's Mach angle and stand-off distance lead to a self-consistent transonic merger speed with Mach 1.06. The region hosting the Faraday depth enhancement shows a decrement in both total and polarised intensity. We fail to identify a satisfactory explanation for this; further observations are warranted. Generally, our study illustrates the scientific returns that can be expected from all-sky grids of discrete sources generated by forthcoming all-sky radio surveys.
Comment: Accepted for publication in PASA. 27 pages, 14 figures, 1 table