There are some spectroscopic studies you may try. If your peptide has Trp/Tyr you may go for fluorescence quenching study. If not you can monitor the absorption change of DNA upon addition of peptide. You may also use some fluorescent dyes (intercalating/groove binding) to saturate DNA and then perform a fluorescence quenching study.

If you can add a fluorescent label to the peptide, binding at nM concentrations easily followed by fluroescence polariztion

In addition to spectroscopic methods, polyacrylamide gel electrophoresis would be another option that will give a clear view of the complex(ex) that are being formed in solution. If the plasmid itself is not relevant for your experiment, you can replace it with short oligonucleotides; this should help with the precipitation.

ITC usually requires higher concentrations than fluorescence measurements described by Uttam and William, so those can be a good option too.

Circular dicrhoism titrations may be helpful for thta.