Context. The 11.99 ms pulsar PSR J1618−3921 orbits a He white dwarf companion of probably low mass with a period of 22.7 d. The pulsar was discovered in a survey of the intermediate Galactic latitudes at 1400 MHz that was conducted with the Parkes radio telescope in the late 1990s. Although PSR J1618−3921 was discovered more than 15 years ago, only limited information has been published about this pulsar, which has a surprisingly high orbital eccentricity (e ≃ 0.027) considering its high spin frequency and the likely low mass of the companion. Aims. The focus of this work is a precise measurement of the spin and the astrometric and orbital characteristics of PSR J1618−3921. This was done with timing observations made at the Nançay Radio Telescope from 2009 to 2017. Methods. We analyzed the timing data recorded at the Nançay Radio Telescope over several years to characterize the properties of PSR J1618−3921. A rotation ephemeris for this pulsar was obtained by analyzing the arrival times of the radio pulses at the telescope. Results. We confirm the unusual eccentricity of PSR J1618−3921 and discuss several hypotheses regarding its formation in the context of other discoveries of recycled pulsars in eccentric orbits.