Natural fatty acids such as sodium oleate form highly viscous supramolecular complexes with long-chain cationic surfactants through cooperative self-assembly. Here we report the rheological behavior of linear and branched wormlike micelles formed in mixtures of cetyltrimethylammonium bromide (CTAB) and sodium oleate (NaOL). Addition of sodium oleate induces an increase in the axial ratio of the mixed micelles. At a constant mole fraction of the mixture, an increase in total surfactant concentration leads to a transition from linear to branched micelles. Both linear and branched micelles impart viscoelastic behavior to the fluid, and the low-frequency data can be approximated to the Maxwell model. Scaling of the rheological parameters of CTAB-NaOL catanionic mixtures, as a function of concentration, employing dynamic theological measurements has been determined and compared with the predictions of existing scaling laws. The structural transition from linear micelles to the branched micelles in the CTAB NaOL micellar system greatly influences the scaling behavior of shear modulus. The scaling exponent is lower for the branched micelles compared to linear micelles, analogous to those of linear and branched polymer melts. The structural evolution is probed by light scattering and small-angle neutron scattering measurements as well.