  SPIRou is the newest spectropolarimeter and high-precision velocimeter that
has recently been installed at the Canada-France-Hawaii Telescope on Maunakea,
Hawaii. It operates in the near-infrared and simultaneously covers the
0.98-2.35 {\mu}m domain at high spectral resolution. SPIRou is optimized for
exoplanet search and characterization with the radial-velocity technique, and
for polarization measurements in stellar lines and subsequent magnetic field
studies. The host of the transiting hot Jupiter HD 189733 b has been observed
during early science runs. We present the first near-infrared
spectropolarimetric observations of the planet-hosting star as well as the
stellar radial velocities as measured by SPIRou throughout the planetary orbit
and two transit sequences. The planetary orbit and Rossiter-McLaughlin anomaly
are both investigated and modeled. The orbital parameters and obliquity are all
compatible with the values found in the optical. The obtained radial-velocity
precision is compatible with about twice the photon-noise estimates for a K2
star under these conditions. The additional scatter around the orbit, of about
8 m/s, agrees with previous results that showed that the activity-induced
scatter is the dominant factor. We analyzed the polarimetric signal, Zeeman
broadening, and chromospheric activity tracers such as the 1083nm HeI and the
1282nm Pa\b{eta} lines to investigate stellar activity. First estimates of the
average unsigned magnetic flux from the Zeeman broadening of the FeI lines give
a magnetic flux of 290+-58 G, and the large-scale longitudinal field shows
typical values of a few Gauss. These observations illustrate the potential of
SPIRou for exoplanet characterization and magnetic and stellar activity
studies.
