Amphiphilic polymer carriers (PEG–St–R) were prepared from cassava starch and their pH response was investigated. First, hydrophobic tapioca starch polymer (St–R) was prepared with octyl acyl as the hydrophobic group. The hydrophilic group polyethylene glycol (mPEG) was then introduced into the polymer by esterification to produce amphiphilic tapioca starch polymer (PEG–St–R). Its self-assembly behavior was characterized using fluorescent probes. The morphology of PEG–St–R was investigated by transmission electron microscopy (TEM). Loading of the anti-cancer drug curcumin was used to assess the delivery and slow-release performance of the amphiphilic tapioca starch polymer. Cumulative drug release was explored at various pH conditions, with the greatest release from drug-loaded micelles being observed under acidic conditions and stable in a neutral environment. These results provide a theoretical basis for the preparation of pH-responsive nanomicelle carriers, and a platform for the preparation of novel amphiphilic starch-based polymers.