Although cisplatin is highly soluble in DMSO, it is reported to be rendered inactive due to ligand displacement by nucleophilic sulfur of DMSO. You may want to refer to the article attached below for more information.
Article Say No to DMSO: Dimethylsulfoxide Inactivates Cisplatin, Car...
You may use DMF instead of DMSO to prepare a stock solution of cisplatin. Cisplatin in soluble in DMF at approximately 10mg/ml. Further dilutions may be made in 0.9% saline or PBS.
Also, cisplatin is slightly soluble in water at 1mg/ml (with warming). You may use sodium chloride solution in water (154mM NaCl with or without 10mg/ml mannitol) or PBS (with 140mM NaCl) for solubilization prior to culture treatment.