  The high accuracy $\phi $-meson photoproduction data from the CLAS experiment
in Hall~B of Jefferson Laboratory allow us to determine the near-threshold
total cross section of the $\gamma p\to\phi p$ reaction and use it for
evaluating the $\phi p$ scattering length $\alpha_{\phi p}$. These data result
in an absolute value of $|\alpha_{\phi p}| = (0.063\pm 0.010)$~fm, which is
smaller than the typical hadron size. A comparative analysis of $\alpha_{\phi
p}$ with the previously determined scattering lengths for $\omega p$ and
$J/\psi p$ from the A2 and GlueX experiments is performed.
