The space-division multiplexed (SDM) coherent transmission using a multi-core fiber (MCF) is a promising technology for further increasing the capacity of optical communications and interconnects. For broader application of SDM systems, dual-polarization (DP) coherent receivers that can be directly coupled to MCFs without bulky fan-in/fan-out (FIFO) devices and polarization beam splitters (PBSs) are desirable. Unlike intensity-modulation direct-detection (IMDD) receivers, however, scaling a DP coherent receiver to multiple spatial channels in a compact form factor is not straightforward. Here, we propose and demonstrate a compact and scalable surface-normal multi-core DP coherent receiver using an ultrathin dielectric metasurface (MS). The MS is composed of silicon nanoposts on quartz, which are judiciously designed to function as the DP optical hybrids and focusing lenses for all spatial channels. Using the fabricated device, simultaneous homodyne detection of DP 64-ary quadrature-amplitude-modulation signals from a four-core fiber is demonstrated with an error vector magnitude of less than 3% for all spatial/polarization channels from 1530 to 1570 nm. The demonstrated receiver can be assembled into a compact module to enable low-cost SDM coherent receivers without bulky PBS and FIFO devices.