The normalized $^{238}$U(n,f)/$^{235}$U(n,f) cross section ratio has been measured using the NIFFTE fission Time Projection Chamber from the reaction threshold to $30$~MeV. The fissionTPC is a two-volume MICROMEGAS time projection chamber that allows for full three-dimensional reconstruction of fission-fragment ionization profiles from neutron-induced fission. The measurement was performed at the Los Alamos Neutron Science Center, where the neutron energy is determined from neutron time-of-flight. The $^{238}$U(n,f)/$^{235}$U(n,f) ratio reported here is the first cross section measurement made with the fissionTPC, and will provide new experimental data for evaluation of the $^{238}$U(n,f) cross section, an important standard used in neutron-flux measurements. Use of a development target in this work prevented the determination of an absolute normalization, to be addressed in future measurements. Instead, the measured cross section ratio has been normalized to ENDF/B-VIII.$beta$5 at 14.5 MeV.