The Dark matter Experiment using Argon Pulse-shape discrimination (DEAP) has been designed for a direct detection search for particle dark matter using a single-phase liquid argon target. The projected cross section sensitivity for DEAP-3600 to the spin-independent scattering of Weakly Interacting Massive Particles (WIMPs) on nucleons is $10^{-46}~rm{cm}^{2}$ for a 100 GeV/$c^2$ WIMP mass with a fiducial exposure of 3 tonne-years. This paper describes the physical properties and construction of the DEAP-3600 detector.