This work proposes a novel logic device (SkyLogic) based on skyrmions, which are magnetic vortex-like structures that have low depinning current density and are robust to defects. A charge current sent through a polarizer ferromagnet (P-FM) nucleates a skyrmion at the input end of an intra-gate FM interconnect with perpendicular magnetic anisotropy (PMA-FM). The output end of the PMA--FM forms the free layer of an MTJ stack. A spin Hall metal (SHM) is placed beneath the PMA-FM. The skyrmion is propagated to the output end of the PMA-FM by passing a charge current through the SHM. The resistance of the MTJ stack is low (high) when a skyrmion is present (absent) in the free layer, thereby realizing an inverter. A framework is developed to analyze the performance of the SkyLogic device. A circuit-level technique is developed that counters the transverse displacement of skyrmion in the PMA-FM and allows use of high current densities for fast propagation. The design space exploration of the PMA-FM material parameters is performed to obtain an optimal design point. At the optimal point, we obtain an inverter delay of 434 ps with a switching energy of 7.1 fJ.