  We present a study of the central exclusive $\pi^{+} \pi^{-}$ production via
the photoproduction mechanism in nucleon-nucleon collisions. The
photon-pomeron/reggeon and pomeron/reggeon-photon exchanges both for the
$\rho^{0}$ resonance contribution and the Drell-S\"oding contribution are
considered. The amplitudes for the processes are formulated in terms of
vertices respecting the standard crossing and charge-conjugation relations of
Quantum Field Theory. The coupling parameters of tensor pomeron and reggeon
exchanges are fixed based on the H1 and ZEUS experimental data for the $\gamma
p \to \rho^{0} p$ reaction. We present first predictions of this mechanism for
the $pp \to pp \pi^{+} \pi^{-}$ reaction being studied at COMPASS, RHIC,
Tevatron, and LHC. We show the influence of the experimental cuts on the
integrated cross section and on various differential distributions for outgoing
particles. Distributions in rapidities and transverse momenta of outgoing
protons and pions as well as correlations in azimuthal angle between them are
presented. We compare the photoproduction contribution to $\pi^{+} \pi^{-}$
distributions with double pomeron/reggeon two-pion continuum. We discuss
whether the high-energy central production of $\rho^{0}$ mesons could be
selected experimentally.
