The tidal disruption of a star by a supermassive black hole leads to a short-lived thermal flare. Despite extensive searches, radio follow-up observations of known thermal stellar tidal disruption flares (TDFs) have not yet produced a conclusive detection. We present a detection of variable radio emission from a thermal TDF, which we interpret as originating from a newly launched jet. The multiwavelength properties of the source present a natural analogy with accretion-state changes of stellar mass black holes, which suggests that all TDFs could be accompanied by a jet. In the rest frame of the TDF, our radio observations are an order of magnitude more sensitive than nearly all previous upper limits, explaining how these jets, if common, could thus far have escaped detection.