Photonic wire bonding is demonstrated to enable highly efficient coupling between multi-core fibers and planar silicon photonic circuits. The technique relies on in-situ fabrication of three-dimensional interconnect waveguides between the fiber facet and tapered silicon-on-insulator waveguides. Photonic wire bonding can easily compensate inaccuracies of core placement in the fiber cross-section, does not require active alignment, and is well suited for automated fabrication. We report on the design, on fabrication, and on characterization of photonic wire bonds. In a proof-of-principle experiment, a four-core fiber is coupled to a silicon photonic chip, leading to measured coupling losses as small as 1.7 dB.