  We present a chemo-dynamical study of the Orphan stellar stream using a
catalog of RR~Lyrae pulsating variable stars for which photometric,
astrometric, and spectroscopic data are available. Employing low-resolution
spectra from the Sloan Digital Sky Survey (SDSS), we determined line-of-sight
velocities for individual exposures and derived the systemic velocities of the
RR~Lyrae stars. In combination with the stars' spectroscopic metallicities and
\textit{Gaia} EDR3 astrometry, we investigated the northern part of the Orphan
stream. In our probabilistic approach, we found 20 single mode RR~Lyrae
variables likely associated with the Orphan stream based on their positions,
proper motions, and distances. The acquired sample permitted us to expand our
search to nonvariable stars in the SDSS dataset, utilizing line-of-sight
velocities determined by the SDSS. We found 54 additional nonvariable stars
linked to the Orphan stream. The metallicity distribution for the identified
red giant branch stars and blue horizontal branch stars is, on average,
$-2.13\pm0.05$ dex and $-1.87\pm0.14$ dex, with dispersions of 0.23 and
0.43dex, respectively. The metallicity distribution of the RR~Lyrae variables
peaks at $-1.80\pm0.06$ dex and a dispersion of 0.25dex. Using the collected
stellar sample, we investigated a possible link between the ultra-faint dwarf
galaxy Grus II and the Orphan stream. Based on their kinematics, we found that
both the stream RR~Lyrae and Grus II are on a prograde orbit with similar
orbital properties, although the large uncertainties on the dynamical
properties render an unambiguous claim of connection difficult. At the same
time, the chemical analysis strongly weakens the connection between both. We
argue that Grus II in combination with the Orphan stream would have to exhibit
a strong inverse metallicity gradient, which to date has not been detected in
any Local Group system.
