Exploring the interaction of nucleic acids with clay minerals is important to understand such issues as the persistence in soils of biomolecules and the appearance of genetic polymers in prebiotic environments. Colloidal dispersions of double stranded DNA and clay nanosheets may also provide interesting model systems to study the statistical physics of mixtures of semi-flexible rods and plates. Here, we show that adding very small amounts of DNA to liquid-crystalline montmorillonite and beidellite smectite clay suspensions strongly widens the isotropic/nematic phase coexistence region. Moreover, a spectroscopic study shows that, upon DNA addition, the first DNA molecules adsorb onto the clay particles. Remarkably, synchrotron small-angle X-ray scattering experiments reveal that the average distance between the clay sheets, in the nematic phase at coexistence, decreases with increasing DNA concentration and that the inhibition of swelling by DNA becomes almost independent of clay concentration. We interpret this DNA-mediated attraction between clay nanosheets by bridging conformations of DNA strands (plates on a string structure). In addition to bridging, DNA chains can form “loops” between sections adsorbed on the same particle, giving rise to sheet repulsions due to protruding loops. This interpretation agrees with the observed inter-clay spacings being dependent only on the DNA concentration.