This Letter reports the first results of a direct dark matter search with the DEAP-3600 single-phase liquid argon (LAr) detector. The experiment was performed 2 km underground at SNOLAB (Sudbury, Canada) utilizing a large target mass, with the LAr target contained in a spherical acrylic vessel of 3600 kg capacity. The LAr is viewed by an array of PMTs, which would register scintillation light produced by rare nuclear recoil signals induced by dark matter particle scattering. An analysis of 4.44 live days (fiducial exposure of 9.87 ton day) of data taken during the initial filling phase demonstrates the best electronic recoil rejection using pulse-shape discrimination in argon, with leakage <1.2×10^{-7} (90% C.L.) between 15 and 31 keV_{ee}. No candidate signal events are observed, which results in the leading limit on weakly interacting massive particle (WIMP)-nucleon spin-independent cross section on argon, <1.2×10^{-44} cm^{2} for a 100 GeV/c^{2} WIMP mass (90% C.L.).