Compact fiber-to-chip couplers play an important role in optical interconnections, especially in data centers. However, the development of couplers has been mostly limited to standard single-mode fibers, with few devices compatible with multicore and multimode fibers. Through the use of state-of-the-art optimization algorithms, we designed a compact dual-polarization coupler to interface chips and dense multicore fibers, demonstrating, for the first time, coupling to both polarizations of all the cores, with measured coupling efficiency of -4.3dB and with a 3 dB bandwidth of 48 nm. The dual-polarization coupler has a footprint of 200µm2 per core, which makes it the smallest fiber-to-chip coupler experimentally demonstrated on a standard silicon-on-insulator platform.