We present a metamaterial consisting of a two-dimensional, asymmetric lattice of crossed nanochannels in fused silica, with channel diameters of 80 nm to 140 nm. When DNA is introduced, it is stretched and linearized. We show that the asymmetry in channel dimensions gives rise to a preferred direction for DNA orientation and a preferred direction for transport under dc electrophoresis. Interestingly, the preferred axis of orientation and transport can be switched by 90 degrees through application of an ac voltage. We explain the results in terms of an energy landscape for polyelectrolytes that consists of entropic and dielectrophoretic contributions and whose strength and sign can be tuned by changing the ac field strength.