In this work the photon beam asymmetry $\Sigma$ for the reaction $\gamma p\to K^+\Sigma^0$(1193) is measured using the GlueX experiment in Hall D at Jefferson Lab. The analysis used data that were collected using a linearly polarized photon beam in the energy range (8.2 - 8.8) GeV incident on a liquid hydrogen target. The beam asymmetries are measured as a function of the Mandelstam variable $t$ and as a single value for the low $u$ region. These are the first exclusive measurements of the photon beam asymmetry $\Sigma$ in this reaction at energies above the baryon resonance region. For the $t$-channel, results are close to unity and show that the reaction is dominated by the natural-parity exchange of the $K^{*}$(892) Regge trajectory as predicted by theoretical models. A value of $\Sigma$ = 0.410$\pm$0.090 is obtained for the $u$-channel and suggests the exchange of both $\Sigma$($J=1/2$) and $Y^{*}$($J=3/2$) trajectory contributions to the production of $K^{+}\Sigma^{0}$.
