Photoproduction of the $omega$ meson on the proton has been experimentally studied near the threshold. The total cross sections are determined at incident energies ranging from 1.09 to 1.15 GeV. The 1/2 and 3/2 spin-averaged scattering length $a_{omega p}$ and effective range $r_{omega p}$ between the $omega$ meson and proton are estimated from the shape of the total cross section as a function of the incident photon energy: $a_{omega p} = left(-0.97^{+0.16_{rm stat}}_{-0.16_{rm stat}}{}^{+0.03_{rm syst}}_{-0.00_{rm syst}}right)+i left(0.07^{+0.15_{rm stat}}_{-0.14_{rm stat}}{}^{+0.17_{rm syst}}_{-0.09_{rm syst}}right)$ fm and $r_{omega p}=left(+2.78^{+0.68_{rm stat}}_{-0.54_{rm stat}}{}^{+0.11_{rm syst}}_{-0.13_{rm syst}}right)+ileft(-0.01^{+0.46_{rm stat}}_{-0.50_{rm stat}}{}^{+0.07_{rm syst}}_{-0.00_{rm syst}}right)$ fm, resulting in a repulsive force. The real and imaginary parts for $a_{omega p}$ and $r_{omega p}$ are determined separately for the first time. A small $P$-wave contribution does not affect the obtained values.
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