We report the first experimental realization of all-optical trapping and manipulation of plasmonic nanowires in three dimensions. The optical beam used for trapping is the Fourier transform of a linearly polarized Bessel beam (termed FT-Bessel). The extended depth of focus of this beam enables the use of a retroreflection geometry to cancel radiation pressure in the beam propagation direction, making it possible to trap highly scattering and absorbing silver nanowires. Individual silver nanowires with lengths of several micrometers can be positioned by the trapping beam with a precision better than 100 nm and are oriented by the polarization of the trapping light with a precision of approximately 1°. Multiple nanowires can be trapped simultaneously in spatially separated maxima of the trapping field. Since trapping in the interferometric FT-Bessel potential is robust in bulk solution and near surfaces, it will enable the controlled assembly of metal nanowires into plasmonic nanostructures.