We present the results of an extensive survey of RR Lyrae (RRL) stars in three fields along the major axis of the Triangulum Galaxy (M33). From images taken with the Advanced Camera for Surveys (ACS) Wide Field Channel on board the Hubble Space Telescope through two passbands (F606W and F814W), we have identified and characterized a total of 119 RRL variables (96 RRab (RR0) and 23 RRc (RR1)) in M33. Using the properties of 83 RRL stars (65 RRab and 18 RRc) in the innermost ACS field (hereafter DISK2), we find mean periods of langP abrang = 0.553 ± 0.008 (error1) ± 0.05 (error2) and langPc rang = 0.325 ± 0.008 (error1) ± 0.05 (error2), where the "error1" value represents the standard error of the mean and the "error2" value is based on the error of an individual RRL period calculated from our synthetic light curve simulations. The distribution of RRab periods and the frequency of RRc stars (Nc = nc /n abc = 0.22) strongly suggest that these RRLs follow the general characteristics of those in Oosterhoff type I Galactic globular clusters. The metallicities of 65 individual RRab stars are calculated from the period-amplitude-metallicity relationship, yielding a mean metallicity of lang[Fe/H]rang = -1.48 ± 0.05 dex, where the uncertainty is the standard error of the mean. The VI minimum-light colors of the RRab stars are used to calculate a mean line-of-sight reddening toward the DISK2 field of langE(V - I)rang = 0.175. By adopting this line-of-sight reddening and using a relation between RRL luminosity and metallicity (MV = 0.23[Fe/H]+0.93), we estimate a mean distance modulus of lang(m - M)0rang = 24.52 ± 0.11 for M33, where the error is the quadratic sum of the uncertainties in the absolute and dereddened V magnitudes of the RRLs. The Oosterhoff I properties of the M33 field RRL stars agree well with those of RRL populations found in the M31 halo consistent with the past interaction history of these two galaxies.Based on observations made with the NASA/ESA Hubble Space Telescope, obtained from the data archive at the Space Telescope Science Institute. STScI is operated by the Association of Universities for Research in Astronomy, Inc. under NASA contract NAS 5-26555.