Stellar rotation is closely linked to both the age and the magnetic activity of stars. Through gyrochronology, studying stellar rotation provides a means to estimate stellar ages and trace the evolution of planetary systems, and it is also a crucial means to constrain and correct stellar activity effects for robust exoplanet detection and characterisation. CARMENES is a dual-channel, high-resolution (ℛ > 80 000) spectrograph that has been highly successful in detecting exoplanets around M-dwarf stars using the radial-velocity technique, and it also enables precise measurements of the projected rotational velocity (v sin i) from spectral line broadening. We present an oversampled convolution method that incorporates a realistic limb-darkening model to determine v sin i from CARMENES spectra by comparing observed spectra with that of a template star. The advantages over existing methods in the literature have been assessed using high-resolution synthetic spectrat that span effective temperatures of 2500─4000 K and projected rotational velocities of up to 50 km s−1. We applied our method to 392 M dwarfs observed with CARMENES and it yielded v sin i measurements (or upper limits at 2 km s−1) with a median relative uncertainty of 6.8%, which is substantially smaller than the 15.4% reported in the literature. This work provides the largest uniform catalogue of v sin i measurements for M dwarfs, including significantly updated values for several targets, along with 36 new targets.