We report measurements of the photon beam asymmetry Σ for the reaction γp→K+Σ0 (1193) using the GlueX spectrometer in Hall D at Jefferson Lab. Data were collected by using a linearly polarized photon beam in the energy range of 8.2–8.8 GeV incident on a liquid hydrogen target. The beam asymmetry Σ was measured as a function of the Mandelstam variable t , and a single value of Σ was extracted for events produced in the u channel. These are the first exclusive measurements of the photon beam asymmetry Σ for the reaction in this energy range. For the t channel, the measured beam asymmetry is close to unity over the t range studied, − t = ( 0.1 – 1.4 ) ( GeV / c ) 2 , with an average value of Σ = 1.00 ± 0.05 . This agrees with theoretical models that describe the reaction via the natural-parity exchange of the K ∗ (892) Regge trajectory. A value of Σ = 0.41 ± 0.09 is obtained for the u channel integrated up to − u = 2.0 ( GeV / c ) 2 .