  We consider the excitation of the nuclear transition ^{229g}Th - ^{229m}Th
near 7.6 eV in singly ionized thorium via an electronic bridge process. The
process relies on the excitation of the electron shell by two laser photons
whose sum frequency is equal to the nuclear transition frequency. This scheme
allows to determine the nuclear transition frequency with high accuracy. Based
on calculations of the electronic level structure of Th^+ which combine the
configuration-interaction method and many-body perturbation theory, we estimate
that a nuclear excitation rate in the range of 10 s^{-1} can be obtained using
conventional laser sources.
