  The addition of an external starshade to the {\it Nancy Grace Roman Space
Telescope} will enable the direct imaging of Earth-radius planets orbiting at
$\sim$1 AU. Classification of any detected planets as Earth-like requires both
spectroscopy to characterize their atmospheres and multi-epoch imaging to trace
their orbits. We consider here the ability of the Starshade Rendezvous Probe to
constrain the orbits of directly imaged Earth-like planets. The target list for
this proposed mission consists of the 16 nearby stars best suited for direct
imaging. The field of regard for a starshade mission is constrained by solar
exclusion angles, resulting in four observing windows during a two-year
mission. We find that for habitable-zone planetary orbits that are detected at
least three times during the four viewing opportunities, their semi-major axes
are measured with a median precision of 7 mas, or a median fractional precision
of 3\%. Habitable-zone planets can be correctly identified as such 96.7\% of
the time, with a false positive rate of 2.8\%. If a more conservative criteria
is used for habitable-zone classification (95\% probability), the false
positive rate drops close to zero, but with only 81\% of the truly Earth-like
planets correctly classified as residing in the habitable zone.
