  We report observations of polarized line and continuum emission from the disk
of TW~Hya using the Atacama Large Millimeter/submillimeter Array. We target
three emission lines, $^{12}$CO (3-2), $^{13}$CO (3-2) and CS (7-6), to search
for linear polarization due to the Goldreich-Kylafis effect, while
simultaneously tracing the continuum polarization morphology at 332\,GHz
(900\,\micron{}), achieving a spatial resolution of 0.5\arcsec{} (30~au). We
detect linear polarization in the dust continuum emission; the polarization
position angles show an azimuthal morphology, and the median polarization
fraction is $\sim$\,0.2\%, comparable to previous, lower frequency
observations. Adopting a `shift-and-stack' technique to boost the sensitivity
of the data, combined with a linear combination of the $Q$ and $U$ components
to account for their azimuthal dependence, we detect weak linear polarization
of $^{12}$CO and $^{13}$CO line emission at a $\sim 10\sigma$ and $\sim
5\sigma$ significance, respectively. The polarization was detected in the line
wings, reaching a peak polarization fraction of $\sim 5\%$ and $\sim 3\%$ for
the two molecules between disk radii of 0.5" and 1". The sign of the
polarization was found to flip from the blue-shifted side of the emission to
the red-shifted side, suggesting a complex, asymmetric polarization morphology.
Polarization is not robustly detected for the CS emission; however, a tentative
signal, comparable in morphology to that found for the $^{12}$CO and $^{13}$CO
emission, is found at a $\lesssim 3\sigma$ significance. We are able to
reconstruct a polarization morphology, consistent with the azimuthally averaged
profiles, under the assumption that this is also azimuthally symmetric, which
can be compared with future higher-sensitivity observations.
