We demonstrate the rapid readout of terahertz orbital angular momentum (OAM) beams using an atomic-vapor-based imaging technique. OAM modes with both azimuthal and radial indices are created using phase-only transmission plates. The beams undergo terahertz-to-optical conversion in an atomic vapor, before being imaged in the far field using an optical CCD camera. In addition to the spatial intensity profile, we also observe the self-interferogram of the beams by imaging through a tilted lens, allowing the sign and magnitude of the azimuthal index to be read out directly. Using this technique, we can reliably read out the OAM mode of low-intensity beams with high fidelity in 10 ms. Such a demonstration is expected to have far-reaching consequences for proposed applications of terahertz OAM beams in communications and microscopy.