SrIrO₃, a Dirac material with a strong spin-orbit coupling (SOC), is a platform for studying topological properties in strongly correlated systems, where its band structure can be modulated by multiple factors, such as crystal symmetry, elements doping, oxygen vacancies, magnetic field, and temperature. Here, we find that the engineered carrier density plays a critical role on the magnetoelectric transport properties of the topological semimetal SrIrO₃. The decrease of carrier density subdues the weak localization and the associated negative magnetoresistance, while enhancing the SOC-induced weak anti-localization. Notably, the sample with the lowest carrier density exhibits high-field positive magnetoresistance, suggesting the presence of a Dirac cone. In addition, the anisotropic magnetoresistance indicates the anisotropy of the electronic structure near the Fermi level. The engineering of carrier density provides a general strategy to control the Fermi surface and electronic structure in topological materials.