We present measurements of the stellar and gaseous velocities in the central 5' of the Local Group spiral M33. The data were obtained with the ARC 3.5m telescope. Blue and red spectra with resolutions from 2 to 4Å covering the principal gaseous emission and stellar absorption lines were obtained along the major and minor axes and six other position angles. The observed radial velocities of the ionized gas along the photometric major axis of M33 remain flat at ~22 km s^{-1} all the way into the center, while the stellar velocities show a gradual rise from zero to 22 km s^{-1} over that same region. The central star cluster is at or very close to the dynamical center, with a velocity that is in accordance with M33's systemic velocity to within our uncertainties. Velocities on the minor axis are non-zero out to about 1' from the center in both the stars and gas. Together with the major axis velocities, they point at significant deviations from circular rotation. The most likely explanation for the bulk of the velocity patterns are streaming motions along a weak inner bar with a PA close to that of the minor axis, as suggested by previously published IR photometric images. The presence of bar imprints in M33 implies that all major Local Group galaxies are barred. The non-circular motions over the inner 200 pc make it difficult to constrain the shape of M33's inner dark matter halo profile. If the non-circular motions we find in this nearby Sc galaxy are present in other more distant late-type galaxies, they might be difficult to recognize. ; Comment: 20 pages, 12 figures, ApJ in press