We present reverberation-mapping (RM) lags and black hole mass measurements using the C IV lambda 1549 broad emission line from a sample of 348 quasars monitored as a part of the Sloan Digital Sky Survey RM Project. Our data span four years of spectroscopic and photometric monitoring for a total baseline of 1300 days, allowing us to measure lags up to similar to 750 days in the observed frame (this corresponds to a rest-frame lag of similar to 300 days in a quasar at z = 1.5 and similar to 190 days at z = 3). We report significant time delays between the continuum and the C IV lambda 1549 emission line in 48.quasars, with an estimated false-positive detection rate of 10%. Our analysis of marginal lag measurements indicates that there are on the order of similar to 100 additional lags that should be recoverable by adding more years of data from the program. We use our measurements to calculate black hole masses and fit an updated C IV radius-luminosity relationship. Our results significantly increase the sample of quasars with C IV RM results, with the quasars spanning two orders of magnitude in luminosity toward the high-luminosity end of the C IV.radius-luminosity relation. In addition, these quasars are located at some of the highest redshifts (z approximate to 1.4-2.8) of quasars with black hole masses measured with RM. This work constitutes the first large sample of C IV RM measurements in more than a dozen quasars, demonstrating the utility of multiobject RM campaigns.