Galactic archaeology largely relies on precise ages of distant evolved stars in
the Milky Way. Nowadays, asteroseismology can deliver ages for many
red giants observed with high-cadence, high-precision
photometric space missions such as CoRoT Kepler K2, TESS, and
soon PLATO. Our aim is to quantify the age uncertainties of currently slowly rotating red giants due to the cumulative effect of their fast rotation
during core-hydrogen burning: their rotation
in earlier evolutionary phases
caused mixing of elements, resulting in heavier helium cores
and the prolongation of their main-sequence lifetime. These rotational
effects are usually ignored when age-dating red giants, despite our knowledge of fast rotation for stars with $M 1.3$\,M$_ odot$. We used a sample of F-type gravito-inertial pulsators ($ stars) with precise asteroseismic estimates of their internal rotation rate from Kepler\/ asteroseismology
and with luminosity estimates from Gaia . For this sample, which includes stars
rotating from nearly zero to
about 60\,<!PCT!> of the critical rate, we computed the cumulative effect on the age in their post-main-sequence evolution caused by rotational mixing on the main sequence. We used stellar model grids with different physical prescriptions that mimic rotational mixing to assess systematic uncertainties on the age. With respect to non-rotating models, the sample of stars, as red giant progenitors reveals age differences up to 5\,<!PCT!> by the time they start hydrogen-shell burning when relying on the theory of rotationally induced diffusive mixing as included in the MIST isochrones. Using rotational mixing based on an advective-diffusive approach that includes meridional circulation leads to an age shift of 20\,<!PCT!> by the time of the tip of the red giant branch. The age-dating of red giants is affected by the cumulative effect of
rotational mixing during the main sequence.
Such rotationally induced age shifts should be taken into
account in addition to other effects if the aim is to
perform Galactic archaeological studies at the highest precision.