A terahertz (THz) waveguide-fed circularly polarised (CP) antipodal exponentially tapered slot antenna (AETSA) is designed, fabricated and measured. This antenna is fed by a WR2.2 rectangular waveguide. The integrated AETSA is fabricated by deep reactive-ion etching on silicon wafers, gold-sputtering and gold-gold thermo-compression bonding. Optimised exponential curves are introduced to the profiles of tapered slots to realise the CP performance. The measured radiation patterns at 490 GHz show beamwidths of 42°and 39°in the 0°-plane and 90°-plane, with low sidelobes. Furthermore, the measured axial ratios (ARs) from 480 to 500 GHz are lower than 2 dB. The THz waveguide-fed CP AETSA has potential to be applied in compact THz imaging, detection and communication systems.