We present a systematic search for tidal disruption events (TDEs) using radio data from the Variables and Slow Transients (VAST) Pilot Survey conducted using the Australian Square Kilometre Array Pathfinder. Historically, TDEs have been identified using observations at X-ray, optical, and ultraviolet wavelengths. After discovery, a few dozen TDEs have been shown to have radio counterparts through follow-up observations. With systematic time-domain radio surveys becoming available, we can now identify new TDEs in the radio regime. A population of radio-discovered TDEs has the potential to provide several key insights including an independent constraint on their volumetric rate. We conducted a search to select variable radio sources with a single prominent radio flare and a position consistent within 2σ of the nucleus of a known galaxy. While TDEs were the primary target of our search, sources identified in this search may also be consistent with active galactic nuclei exhibiting unusual flux density changes at the timescales probed, uncharacteristically bright supernovae, or a population of gamma-ray bursts. We identify a sample of 12 radio-bright candidate TDEs. The timescales and luminosities range from ∼6 to 230 days and ∼1038 to 1041 erg s−1, respectively, consistent with models of radio emission from TDEs that launch relativistic jets. After calculating the detection efficiency of our search using a Monte Carlo simulation of TDEs, and assuming all 12 sources are jetted TDEs, we derive a volumetric rate for jetted TDEs of 0.80−0.23+0.31 Gpc−3 yr−1, consistent with previous empirically estimated rates.