The synchrotron-based small-angle X-ray scattering (SAXS) technique was used to investigate the shear-induced crystallization kinetics of branched/unbranched poly(ethylene terephthalate) (PET). Reactive extrusion of bottle-grade PET with the branching and chain-extension agents pyromellitic dianhydride and pentaerythritol results in enhanced rheological properties, such as higher melt strength and higher viscosity. In this study, six samples of PET were investigated: linear PET [intrinsic viscosity (IV) ≃ 0.76 dm3 g−1]; four branched PETs produced from linear PET by a reactive extrusion technique (IV ≃ 0.86–1.06 dm3 g−1); and a control PET (IV ≃ 0.73 dm3 g−1) extruded under the same conditions without reactive agents. SAXS data were recorded for the PET at the melt temperature and time-resolved SAXS data were recorded following the application of a step shear (53 s−1 for 2 s). As the PET IV was increased, the extent of shear-induced orientation increased, whilst the time taken for the polymer to initiate and complete crystallization decreased.