We report on the results of a time-series photometric survey of NGC 2362, carried out using the CTIO 4-m Blanco telescope and Mosaic-II detector as part of the Monitor project. Rotation periods were derived for 271(*) candidate cluster members over the mass range 0.1~<M/M_{sun}_<~1.2. The rotation period distributions show a clear mass-dependent morphology, qualitatively similar to that in NGC 2264, as would be expected from the age of this cluster. Using models of angular momentum evolution, we show that angular momentum losses over the ~1-5Myr age range appear to be needed in order to reproduce the evolution of the slowest rotators in the sample from the ONC to NGC 2362, as found by many previous studies. By incorporating Spitzer IRAC mid-infrared (mid-IR) measurements, we found that three to four objects showing mid-IR excesses indicative of the presence of circumstellar discs were all slow rotators, as would be expected in the disc regulation paradigm for early pre-main-sequence angular momentum evolution, but this result is not statistically significant at present, given the extremely limited sample size. (*) The abstract indicates 271 clusters, but the actual number is 272.