It has long been hoped that spin liquid states might be observed in materials that realize the triangular-lattice Hubbard model. However, weak spin–orbit coupling and other small perturbations often induce conventional spin freezing or magnetic ordering. Sufficiently strong spin–orbit coupling, however, can renormalize the electronic wavefunction and induce anisotropic exchange interactions that promote magnetic frustration. Here we show that the cooperative interplay of spin-orbit coupling and correlation effects in the triangular-lattice magnet NaRuO₂ produces an inherently fluctuating magnetic ground state. Despite the presence of a charge gap, we find that low-temperature spin excitations generate a metal-like term in the specific heat and a continuum of excitations in neutron scattering, reminiscent of spin liquid states previously found in triangular-lattice organic magnets. Further cooling produces a crossover into a different, highly disordered spin state whose dynamic spin autocorrelation function reflects persistent fluctuations. These findings establish NaRuO₂ as a cousin to organic, Heisenberg spin liquid compounds with a low-temperature crossover in quantum disorder.