Cosmic neutrinos provide a unique window into the otherwise-hidden mechanism of particle acceleration in astrophysical objects. A flux of high-energy neutrinos was discovered in 2013, and the IceCube Collaboration recently associated one high-energy neutrino with a flare from the relativistic jet of an active galaxy pointed towards the Earth. However a combined analysis of many similar active galaxies revealed no excess from the broader population, leaving the vast majority of the cosmic neutrino flux unexplained. Here we present the association of a radio-emitting tidal disruption event (AT2019dsg) with another high-energy neutrino, identified as part of our systematic search for optical counterparts to high-energy neutrinos with the Zwicky Transient Facility (ZTF). The probability of finding any radio-emitting tidal disruption event by chance is 0.5%, while the probability of finding one as bright in bolometric energy flux as AT2019dsg is 0.2%. Our electromagnetic observations can be explained through a multi-zone model, with radio analysis revealing a central engine, embedded in a UV photosphere, that powers an extended synchrotron-emitting outflow. This provides an ideal site for PeV neutrino production. The association suggests that tidal disruption events contribute to the cosmic neutrino flux. Unlike previous work which considered the rare subset of tidal disruption events with relativistic jets, our observations of AT2019dsg suggest an empirical model with a mildly-relativistic outflow.