Aims. Our goal is to calculate the circular velocity curve of the Milky Way, along with corresponding uncertainties that quantify various sources of systematic uncertainty in a self-consistent manner. Methods. The observed rotational velocities are described as circular velocities minus the asymmetric drift. The latter is described by the radial axisymmetric Jeans equation. We thus reconstruct the circular velocity curve between Galactocentric distances from 5 kpc to 14 kpc using a Bayesian inference approach. The estimated error bars quantify uncertainties in the Sun’s Galactocentric distance and the spatial-kinematic morphology of the tracer stars. As tracers, we used a sample of roughly 0.6 million stars on the red giant branch stars with six-dimensional phase-space coordinates from Gaia Data Release 3 (DR3). More than 99% of the sample is confined to a quarter of the stellar disc with mean radial, rotational, and vertical velocity dispersions of (35 ± 18) km s−1, (25 ± 13) km s−1, and (19 ± 9) km s−1, respectively. Results. We find a circular velocity curve with a slope of 0.4 ± 0.6 km s−1 kpc−1, which is consistent with a flat curve within the uncertainties. We further estimate a circular velocity at the Sun’s position of vc(R0) = 233 ± 7 km s−1 and that a region in the Sun’s vicinity, characterised by a physical length scale of ∼1 kpc, moves with a bulk motion of VLSR = 7 ± 7 km s−1. Finally, we estimate that the dark matter (DM) mass within 14 kpc is log10 MDM(R < 14kpc)/ M⊙ =(11.2+2.0-2.3) and the local spherically averaged DM density is ρDM(RO)=(0.41+0.10-0.09) GeV cm-3 = (0.011+0.003-0.002) M⊙pc-3. In addition, the effect of biased distance estimates on our results is assessed.