It sounds like what you want to do is measure the effects of the intercalating agent on cell proliferation, and not specifically measure the extent of DNA intercalation.  In which case, simply treat it like any other small molecule inhibitor of cell growth - plate your cells, treat them with assorted concentrations of the drug, and count the cells at the end.  You can count manually on a hemacytometer, or automatically with a counter instrument.  If you prefer proliferation dyes, that should work too, though I'd stay away from Brdu and the like, since those interact with genetic material, and the readout might be skewed by your drug.  However, metabolic dyes, such as MTT or Alamar Blue, should give similar results while having a lesser chance of being interfered with by your intercalating reagent.

William P Katt, 

Thank you for the suggestions but I have already done MTT LDH and apoptosis (I have attached )experiments and found that my drug has very anti proliferative effect and very good pro apoptotic effect, right now I want study the mechanisms by which the activity is taking place in a cell. To that extend I want to know which method or assay has to be performed to know the exact mechanism. 

You may try caspase assay (if apoptotic mechanism is interesting) or you may try to use promega (PoweQuant) or thermo (Human trio) in order to evaluate the effect of DNA damage by your drug. Intercalation finaly results in DNA degradation, that is what they measure.