  We investigate the role driven by the scalar meson $\sigma$ exchange in the
photoproduction of the vector meson $\phi$(1020) off a proton by using a
Reggeized model. Based on the $\pi^0(135)+\sigma(500)+f_2(1270)$+Pomeron
exchanges, we demonstrate that the $\sigma$ exchange plays the role to
reproduce the bump structure at the forward angle in the differential cross
section as well as the peaking behavior in the total cross section observed in
the CLAS Collaboration. We also discuss the possible observation of the scaled
cross section $s^7d\sigma /dt$ at the production angle $\theta=90^{\circ}$ from
the CLAS data. It is found that the axial vector meson $f_1(1285)$ exchange
with the trajectory $\alpha_{f_1}(t)=0.028\,t+0.9\pm0.2$ arising from the axial
anomaly of the QCD vacuum plays the role to clarify the scaling up to 5 GeV.
