Arbitrary manipulation of broadband terahertz waves with flexible polarization shaping at the source has great potential in expanding numerous applications, such as imaging, information encryption, and all-optical coherent control of terahertz nonlinear phenomena. Topological insulators featuring unique spin-momentum–locked surface state have already exhibited very promising prospects in terahertz emission, detection, and modulation, which may lay a foundation for future on-chip topological insulator-based terahertz systems. However, polarization-shaped terahertz emitters based on topological insulators with an arbitrarily manipulated temporal evolution of the amplitude and the electric-field vector direction have not yet been explored. We systematically investigated the terahertz radiation from topological insulator Bi₂Te₃ nanofilms driven by femtosecond laser pulses and successfully realized the generation of efficient chiral terahertz waves with controllable chirality, ellipticity, and principal axis. The convenient engineering of the chiral terahertz waves was interpreted by a photogalvanic effect (PGE)-induced photocurrent, while the linearly polarized terahertz waves originated from linear PGE-induced shift currents. Our work not only provides further understanding of femtosecond coherent control of ultrafast spin currents but also describes an effective way to generate spin-polarized terahertz waves at the source.