  We investigate the feasibility of measuring the proton charge radius through
dimuon photoproduction off a proton target. Our findings indicate that the
Bethe-Heitler mechanism, which dominates at small momentum transfers, allows
for an extraction of the proton electromagnetic form factors in the extremely
low $Q^2$ region below $10^{-3}$ GeV$^2$ in the spacelike region, when the
incident photon beam energy exceeds several hundred MeV. The optimal
kinematical region and a sensitivity study of the proton charge radius from
dimuon photoproduction are presented. Such a measurement is expected to provide
an alternative to the elastic muon-proton scattering measurements such as MUSE
at PSI and AMBER at CERN.
