We go on paving the way for the study of Earth-like exoplanets around M-type dwarfs stars by measuring the rotation periods of stars observed by the CARMENES survey using TESS data. This study will help to distinguish exoplanet radial-velocity signals from the ones produced by features on the rotating features in the stellar atmosphere. We looked for signals in the photometric time series of 352 CARMENES M dwarfs of the guaranteed time observations GTO sample covered by the first 26 TESS sectors. We collected either SAP (Simple Aperture Photometry) or PDCSAP (Pre-search Data Conditioning SAP) time series for 210 stars, and custom extracted the light curves for a further 32 stars from the FFI (Full Frame Images). We measured 69 rotational periods between 0.12 d and 13.20 d of which 23 are new. With those periods in hand, we studied the distribution of angular momenta of stellar systems with and without planets.