We present a new periodogram for periodicity detection in one-dimensional time-series data from scanning astrometry space missions, like Hipparcos or Gaia. The periodogram is non-parametric and does not rely on a full or approximate orbital solution. Since no specific properties of the periodic signal are assumed, the method is expected to be suitable for the detection of various types of periodic phenomena, from highly eccentric orbits to periodic variability-induced movers. The periodogram is an extension of the phase-distance correlation periodogram (PDC) we introduced in previous papers based on the statistical concept of distance correlation. We demonstrate the performance of the periodogram using publicly available Hipparcos data, as well as simulated data. We also discuss its applicability for Gaia epoch astrometry, to be published in the future data release 4 (DR4).