We present reverberation mapping results for the MgII 2800 A broad emission line in a sample of 193 quasars at 0.35<z<1.7 with photometric and spectroscopic monitoring observations from the Sloan Digital Sky Survey Reverberation Mapping project during 2014 - 2017. We find significant time lags between the MgII and continuum lightcurves for 57 quasars and define a gold sample of 24 quasars with the most reliable lag measurements. We estimate false-positive rates for each lag that range from 1-24%, with an average false-positive rate of 11% for the full sample and 8% for the gold sample. There are an additional ~40 quasars with marginal MgII lag detections which may yield reliable lags after additional years of monitoring. The MgII lags follow a radius -- luminosity relation with a best-fit slope that is consistent with alpha=0.5 but with an intrinsic scatter of 0.36dex that is significantly larger than found for the Hb radius -- luminosity relation. For targets with SDSS-RM lag measurements of other emission lines, we find that our MgII lags are similar to the Hb lags and ~2-3 times larger than the CIV lags. This work significantly increases the number of MgII broad-line lags and provides additional reverberation-mapped black hole masses, filling the redshift gap at the peak of supermassive black hole growth between the Hb and CIV emission lines in optical spectroscopy.
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