The beam-spin asymmetry, Sigma, for the reaction gamma d -\u3e pn has been measured using the CEBAF Large Acceptance Spectrometer (CLAS) at the Thomas Jefferson National Accelerator Facility (JLab) for six photon-energy bins, between 1.1 and 2.3 GeV, and proton angles in the center-of-mass frame, theta(c.m.), between 25 degrees and 160 degrees. These are the first measurements of beam-spin asymmetries at theta(c.m.) = 90. for photon-beam energies above 1.6 GeV, and the first measurements for angles other than theta(c.m.) = 90 degrees. The angular and energy dependence of Sigma is expected to aid in the development of QCD-based models to understand the mechanisms of deuteron photodisintegration in the transition region between hadronic and partonic degrees of freedom, where both effective field theories and perturbative QCD cannot make reliable predictions