Polydisperse rhodium nanoparticles have recently shown promise for ultraviolet (UV) plasmonics, but controlling the size and morphology of metal nanoparticles is essential for tuning surface plasmon resonances. Here we report the use of slow-injection polyol methods to synthesize monodisperse Rh nanocubes with unprecedentedly large sizes and slightly concave faces. The associated local surface plasmon resonances (LSPRs) red-shifted with increasing sizes in the UV region from deep UV to around 400 nm, consistent with numerical simulations. UV illumination of p-aminothiophenol attached to the Rh nanocubes generated surface-enhanced Raman spectra and accelerated photo-decomposition, and these enhancements were largest for nanocubes whose LSPR was resonant with the UV laser. The lack of a native oxide coating, the precise control of nanocube size and morphology demonstrated here, and the ability to tune the surface plasmon resonance from the deep UV to near UV spectral region, make rhodium a compelling choice for UV plasmonic applications.