  Weak gravitational lensing is one of the most promising cosmological probes
to constrain dark matter, dark energy, and the nature of gravity at cosmic
scales. Intrinsic alignments (IAs) of galaxies have been recognized as one of
the most serious systematic effects facing gravitational lensing. Such
alignments must be isolated and removed to obtain a pure lensing signal.
Furthermore, the alignments are related to the processes of galaxy formation,
so their extracted signal can help in understanding such formation processes
and improving their theoretical modeling. We report in this Letter the first
detection of the gravitational shear--intrinsic shape (GI) correlation and the
intrinsic shape--galaxy density (Ig) correlation using the self-calibration
method in a photometric redshift survey. These direct measurements are made
from the KiDS-450 photometric galaxy survey with a significance of 3.65$\sigma$
in the third bin for the Ig correlation, and 3.51$\sigma$ for the GI
cross-correlation between the third and fourth bins. The self-calibration
method uses the information available from photometric surveys without needing
to specify an IA model and will play an important role in validating IA models
and IA mitigation in future surveys such as the Rubin Observatory Legacy Survey
of Space and Time, Euclid, and WFIRST.
