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.

You can use Microscale Thermophoresis (MST), it is a free solution method like ITC but only needs 1/1000 of sample and MST can measure affinities from Kd=10pM to Kd=10mM. MST allows you to optimize your assay conditions very easily and without consuming much material. Actually people are often using MST for assays not possible with ITC.

You can find descriptions of MST studies of peptide-DNA interactions here:

http://link.springer.com/protocol/10.1007/978-1-61779-424-7_18#page-1