What kind of interaction are you looking for? You probably will have some complex formation between nitrogen atoms of the DNA and the Nickel atoms which may replace Chloride as the ligand.
The Nickel UV-Vis is sensitive towards the coordination geometry, circular dichroism may add some chirality information to that. If that's what you're looking for, check out "Tanabe-Sugano diagrams" and associated literature.
If you want to see influences on bond strengths, infrared spectroscopy might be the tool of choice. There is also IR-CD spectroscopy, but I have never read into it.
If your Ni-DNA complex is paramagnetic, EPR spectroscopy would be an option, while if it's diamagnetic, you can do 61Ni NMR.