The realization of a table-top tunable deep-ultraviolet (UV) laser source with excellent noise properties would significantly benefit the scientific community, particularly within imaging and spectroscopic applications, where source noise has a crucial role. Here we provide a thorough characterization of the pulse-to-pulse relative intensity noise (RIN) of such a deep-UV source based on an argon (Ar)-filled anti-resonant hollow-core (AR HC) fiber. Suitable pump pulses are produced using a compact commercially available laser centered at 1030 nm with a pulse duration of 400 fs, followed by a nonlinear compression stage that generates pulses with 30 fs duration, 24.2 μJ energy at 100 kHz repetition rate and a RIN of < 1%. Pump pulses coupled into the AR HC fiber undergo extreme spectral broadening creating a supercontinuum, leading to efficient energy transfer to a phase-matched resonant dispersive wave (RDW) in the deep-UV spectral region. The center wavelength of the RDW could be tuned between 236 and 377 nm by adjusting the Ar pressure in a 140 mm length of fiber. Under optimal pump conditions the RIN properties were demonstrated to be exceptionally good, with a value as low as 1.9% at ~ 282 nm. The RIN is resolved spectrally for the pump pulses, the generated RDW and the broadband supercontinuum. These results constitute the first broadband RIN characterization of such a deep-UV source and provide a significant step forward towards a stable, compact and tunable laser source for applications in the deep-UV spectral region.