We present a deep near-infrared spectrum of the Orion Bar Photodissociation Region (PDR) taken with the Immersion Grating INfrared Spectrometer (IGRINS) on the 2.7m telescope at the McDonald Observatory. IGRINS has high spectral resolution (R~45000) and instantaneous broad wavelength coverage (1.45-2.45{mu}m), enabling us to detect 87 emission lines from rovibrationally excited molecular hydrogen (H_2_) that arise from transitions out of 69 upper rovibration levels of the electronic ground state. These levels cover a large range of rotational and vibrational quantum numbers and excitation energies, making them excellent probes of the excitation mechanisms of H_2_ and physical conditions within the PDR. The Orion Bar PDR is thought to consist of cooler high density clumps or filaments (T=50-250K, n_H_=10^5^-10^7^cm^-3^) embedded in a warmer lower density medium (T=250-1000K, n_H_=10^4^-10^5^cm^-3^). We fit a grid of constant temperature and density Cloudy models, which recreate the observed H_2_ level populations well, to constrain the temperature to a range of 600-650 K and the density to n_H_=2.5x10^3^-10^4^cm^-3^. The best-fit model gives T=625K and n_H_=5x10^3^cm^-3^. This well-constrained warm temperature is consistent with kinetic temperatures found by other studies for the Orion Bar's lower density medium. However, the range of densities well fit by the model grid is marginally lower than those reported by other studies. We could be observing lower density gas than the surrounding medium, or perhaps a density-sensitive parameter in our models is not properly estimated.