  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.
