We present a low-frequency (170\textendash200\,MHz) search for prompt radio emission associated with the long GRB 210419A using the rapid-response mode of the Murchison Widefield Array (MWA), triggering observations with the Voltage Capture System (VCS) for the first time. The MWA began observing GRB 210419A within 89\,s of its detection by \textit{Swift}, enabling us to capture any dispersion delayed signal emitted by this GRB for a typical range of redshifts. We conducted a standard single pulse search with a temporal and spectral resolution of $100\,\upmu$s and 10\,kHz over a broad range of dispersion measures from 1 to $5000\,\text{pc}\,\text{cm}^{-3}$, but none were detected. However, fluence upper limits of $77\text{--}224$\,Jy\,ms derived over a pulse width of $0.5\text{--}10$\,ms and a redshift of $0.6Comment: Accepted for publication in MNRAS