We report measurements of the photon beam asymmetry $Sigma$ for the reaction $vec{gamma} pto K^+Sigma^0$(1193) using the GlueX spectrometer in Hall D at Jefferson Lab. Data were collected 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 $Sigma$ was measured as a function of the Mandelstam variable $t$, and a single value of $Sigma$ was extracted for events produced in the $u$-channel. These are the first exclusive measurements of the photon beam asymmetry $Sigma$ 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 $Sigma = 1.00pm 0.05$. This agrees with theoretical models that describe the reaction via the natural-parity exchange of the $K^{*}$(892) Regge trajectory. A value of $Sigma = 0.41 pm 0.09$ is obtained for the $u$-channel integrated up to $-u=2.0$~(GeV/$c$)$^{2}$.
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