Dispersion among the light elements is common in globular clusters (GCs), while dispersion among heavier elements is less common. We present detection of r-process dispersion relative to Fe in 19 red giants of the metal-poor GC M92. Using spectra obtained with the Hydra multi-object spectrograph on the WIYN Telescope at Kitt Peak National Observatory, we derive differential abundances for 21 species of 19 elements. The Fe-group elements, plus Y and Zr, are homogeneous at a level of 0.07-0.16 dex. The heavy elements La, Eu, and Ho exhibit clear star-to-star dispersion spanning 0.5-0.8 dex. The abundances of these elements are correlated with one another, and we demonstrate that they were produced by r-process nucleosynthesis. This r-process dispersion is not correlated with the dispersion in C, N, or Na in M92, indicating that r-process inhomogeneities were present in the gas throughout star formation. The r-process dispersion is similar to that previously observed in the metal-poor GC M15, but its origin in M15 or M92 is unknown at present.