Refined astrometry measurements allow us to detect large-scale deviations from isotropy through real-time observations of changes in the angular separation between sources at cosmic distances. This "cosmic parallax" effect is a powerful consistency test of the Friedmann-Robertson-Walker metric and may set independent constraints on cosmic anisotropy. We apply this novel general test to Lemaitre-Tolman-Bondi cosmologies with off-center observers and show that future satellite missions such as Gaia might achieve accuracies that would put limits on the off-center distance which are competitive with cosmic microwave background dipole constraints.