The halide double perovskite Cs2AgBiBr6 has emerged as a promising nontoxic alternative to the lead halide perovskites APbX3 (A = organic cation or Cs; X = I or Br). Here, we perform high-pressure synchrotron X-ray total scattering on Cs2AgBiBr6 and discover local disorder that is hidden from conventional Bragg analysis. While our powder diffraction data show that the average structure remains cubic up to 2.1 GPa, analysis of the X-ray pair distribution function reveals that the local structure is better described by a monoclinic space group, with significant distortion within the Ag-Br and Bi-Br octahedra and off-centering of the Cs atoms. By tracking the distribution of interatomic Cs-Br distances, we find that the local disorder is enhanced upon compression, and we corroborate these results with molecular dynamics simulations. The observed local disorder affords new understanding of this promising material and potentially offers a new parameter to tune in halide perovskite lattices.