  Photoproduction of $K^*$ vector mesons off nucleon is investigated within the
Regge framework where the electromagnetic vertex of $\gamma K^*K^*$ fully takes
into account the magnetic dipole and electric quadrupole moments of spin-1
$K^*$ vector meson. The $t$-channel $K^*(892)$, $K(494)$ and $\kappa(800)$
meson exchanges are considered for the analysis of the production mechanism.
The experimentally observed rapid decrease of the cross sections for the
$\gamma p \to K^{*+} \Lambda$ reaction beyond the resonance region is well
reproduced by the dominance of the exchange of $K$-meson trajectory. The role
of the scalar $\kappa$-meson trajectory is found to be minor in both $\gamma p$
and $\gamma n$ reactions. The cross sections for the $\gamma n \to K^{*0}
\Lambda$ reaction are predicted to be about twice those of the $\gamma p \to
K^{*+}\Lambda$ reaction. The role of the $K^*$ electromagnetic multipoles and
the proton anomalous magnetic moment is studied through the total and
differential cross sections and spin/parity asymmetries. We suggest the
measurement of the photon polarization asymmetry as a tool for identifying the
role of the magnetic dipole and electric quadrupole moments of the $K^*$ vector
meson.
