We report the discovery of GJ 3929 b, a hot Earth-sized planet orbiting the nearby M3.5 V dwarf star, GJ 3929 (G 180-18, TOI-2013). Joint modelling of photometric observations from TESS sectors 24 and 25 together with 73 spectroscopic observations from CARMENES and followup transit observations from SAINT-EX, LCOGT, and OSN yields a planet radius of R b = 1.150 ± 0.040 R ⊕ , a mass of M b = 1.21 ± 0.42 M ⊕ , and an orbital period of P b = 2.616 274 5 ± 0.000 003 0 d. The resulting density of ρ b = 4.4 ± 1.6 g cm −3 is compatible with the Earth's mean density of about 5.5 g cm −3 . Due to the apparent brightness of the host star (J = 8.7 mag) and its small size, GJ 3929 b is a promising target for atmospheric characterisation with the JWST. Additionally, the radial velocity data show evidence for another planet candidate with P [c] = 14.303 ± 0.035 d, which is likely unrelated to the stellar rotation period, P rot = 122 ± 13 d, which we determined from archival HATNet and ASAS-SN photometry combined with newly obtained TJO data.