The first high-statistics cross sections for the reactions $\gamma p \to
K^{*+} \Lambda$ and $\gamma p \to K^{*+} \Sigma^0$ were measured using the CLAS
detector at photon energies between threshold and 3.9 GeV at the Thomas
Jefferson National Accelerator Facility. Differential cross sections are
presented over the full range of the center-of-mass angles,
$\theta^{CM}_{K^{*+}}$, and then fitted to Legendre polynomials to extract the
total cross section. Results for the $K^{*+}\Lambda$ final state are compared
with two different calculations in an isobar and a Regge model, respectively.
Theoretical calculations significantly underestimate the $K^{*+} \Lambda$ total
cross sections between 2.1 and 2.6 GeV, but are in better agreement with
present data at higher photon energies.
