The star Kepler-1625 recently attracted considerable attention when an analysis of the stellar photometric time series from the Kepler mission was interpreted as showing evidence of a large exomoon around the transiting Jupiter-sized planet candidate Kepler-1625b. We aim to detect the radial velocity (RV) signal imposed by Kepler-1625b (and its putative moon) on the host star or, as the case may be, determine an upper limit on the mass of the transiting object. We took a total of 22 spectra of Kepler-1625 using CARMENES, 20 of which were useful. Observations were spread over a total of seven nights between October 2017 and October 2018, covering $125%$ of one full orbit of Kepler-1625b. We used the automatic Spectral Radial Velocity Analyser (SERVAL) pipeline to deduce the stellar RVs and uncertainties. Then we fitted the RV curve model of a single planet on a Keplerian orbit to the observed RVs using a $chi^2$ minimisation procedure. We derive upper limits on the mass of Kepler-1625b under the assumption of a single planet on a circular orbit. In this scenario, the $1,sigma$, $2,sigma$, and $3,sigma$ confidence upper limits for the mass of Kepler-1625b are $2.90,M_{rm J}$, $7.15,M_{rm J}$, and $11.60,M_{rm J}$, respectively. We present strong evidence for the planetary nature of Kepler-1625b, making it the 10th most long-period confirmed planet known today. Our data does not answer the question about a second, possibly more short-period planet that could be responsible for the observed transit timing variation of Kepler-1625b.
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