A precise determination of the local dark matter density and an accurate control over the corresponding uncertainties are of paramount importance for dark matter (DM) searches. Using very recent high-resolution numerical simulations of a Milky Way like object, we study the systematic uncertainties that affect the determination of the local dark matter density based on dynamical measurements in the Galaxy. In particular, extracting from the simulation with baryons the orientation of the Galactic stellar disk with respect to the DM distribution, we study the DM density for an observer located at ˜8kpc from the Galactic center on the stellar disk, ρ0. This quantity is found to be always larger than the average density in a spherical shell of the same radius ρ¯0, which is the quantity inferred from dynamical measurements in the Galaxy, and to vary in the range ρ0/ρ¯0=1.01-1.41. This suggests that the actual dark matter density in the solar neighborhood is on average 21% larger than the value inferred from most dynamical measurements, and that the associated systematic errors are larger than the statistical errors recently discussed in the literature.