  DNA origami is a modular platform for the combination of molecular and
colloidal components to create optical, electronic, and biological devices.
Integration of such nanoscale devices with microfabricated connectors and
circuits is challenging: large numbers of freely diffusing devices must be
fixed at desired locations with desired alignment. We present a DNA origami
molecule whose energy landscape on lithographic binding sites has a unique
maximum. This property enables device alignment within 3.2$^{\circ}$ on
SiO$_2$. Orientation is absolute (all degrees of freedom are specified) and
arbitrary (every molecule's orientation is independently specified). The use of
orientation to optimize device performance is shown by aligning fluorescent
emission dipoles within microfabricated optical cavities. Large-scale
integration is demonstrated via an array of 3,456 DNA origami with 12 distinct
orientations, which indicates the polarization of excitation light.
