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 enabled device alignment within 3.2 degrees on silica surfaces. Orientation was absolute (all degrees of freedom were specified) and arbitrary (the orientation of every molecule was independently specified). The use of orientation to optimize device performance was shown by aligning fluorescent emission dipoles within microfabricated optical cavities. Large-scale integration was demonstrated with an array of 3456 DNA origami with 12 distinct orientations that indicated the polarization of excitation light.