We present a detailed study of stellar rotation in the massive 1.5 Gyr old cluster NGC 1846 in the Large Magellanic Cloud. Similar to other clusters at this age, NGC 1846 shows an extended main-sequence turn-off (eMSTO), and previous photometric studies have suggested it could be bimodal. In this study, we use MUSE integral-field spectroscopy to measure the projected rotational velocities (vsin i) of around 1400 stars across the eMSTO and along the upper main sequence of NGC 1846. We measure vsin i values up to similar to 250 km s(-1) and find a clear relation between the vsin i of a star and its location across the eMSTO. Closer inspection of the distribution of rotation rates reveals evidence for a bimodal distribution, with the fast rotators centred around v sin i = 140 km s(-1) and the slow rotators centred around v sin i = 60 km s(-1). We further observe a lack of fast rotating stars along the photometric binary sequence of NGC 1846, confirming results from the field that suggest that tidal interactions in binary systems can spin-down stars. However, we do not detect a significant difference in the binary fractions of the fast and slowly rotating sub-populations. Finally, we report on the serendipitous discovery of a planetary nebula associated with NGC 1846.