We present the Sydney Radio Star Catalogue, a new catalogue of stars detected at megahertz to gigahertz radio frequencies. It consists of 839 unique stars with 3 405 radio detections, more than doubling the previously known number of radio stars. We have included stars from large area searches for radio stars found using circular polarisation searches, cross-matching, variability searches, and proper motion searches as well as presenting hundreds of newly detected stars from our search of Australian SKA Pathfinder observations. The focus of this first version of the catalogue is on objects detected in surveys using SKA precursor and pathfinder instruments; however, we will expand this scope in future versions. The 839 objects in the Sydney Radio Star Catalogue are distributed across the whole sky and range from ultracool dwarfs to Wolf-Rayet stars. We demonstrate that the radio luminosities of cool dwarfs are lower than the radio luminosities of more evolved sub-giant and giant stars. We use X-ray detections of 530 radio stars by the eROSITA soft X-ray instrument onboard the Spectrum Roentgen Gamma spacecraft to show that almost all of the radio stars in the catalogue are over-luminous in the radio, indicating that the majority of stars at these radio frequencies are coherent radio emitters. The Sydney Radio Star Catalogue can be found in Vizier or at https://radiostars.org.