The exclusive reaction γp→K(+)π(-)Σ(+) was measured for the first time using linearly polarized photons at beam energies from 1.85 to 2.96 GeV. Angular distributions in the rest frame of the K(+)π(-) system were fitted to extract spin-density matrix elements of the K(*0) decay. The measured parity spin asymmetry shows that natural-parity exchange is dominant in this reaction. This result clearly indicates the need for t-channel exchange of the κ(800) scalar meson.