We report 272 radial velocities for 19 RR Lyrae variables. For most of the stars we have radial velocities for the complete pulsation cycle. These data are used to determine robust center--of--mass radial velocities that have been compared to values from the literature in a search for evidence of binary systems. Center--of--mass velocities were determined for each star using Fourier Series and Template fits to the radial velocities. Our center--of--mass velocities have uncertainties from $pm0.16$ km s$^{-1}$ to $pm$2.5 km s$^{-1}$, with a mean uncertainty of $pm$0.92 km s$^{-1}$. We combined our center--of--mass velocities with values from the literature to look for deviations from the mean center--of--mass velocity of each star. Fifteen RR Lyrae show no evidence of binary motion (BK And, CI And, Z CVn, DM Cyg, BK Dra, RR Gem, XX Hya, SZ Leo, BX Leo, TT Lyn, CN Lyr, TU Per, U Tri, RV UMa, and AV Vir). In most cases this conclusion is reached due to the sporadic sampling of the center--of--mass velocities over time. Three RR Lyrae show suspicious variation in the center--of--mass velocities that may indicate binary motion but do not prove it (SS Leo, ST Leo, and AO Peg). TU UMa was observed by us near a predicted periastron passage (at 0.14 in orbital phase) but the absence of additional center--of--mass velocities near periastron make the binary detection, based on radial velocities alone, uncertain. Two stars in our sample show $Hgamma$ emission in phases 0.9--1.0: SS Leo and TU UMa.
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