[en] Polychromatic synchrotron x-ray microdiffraction is used to determine the epitaxy of YBa₂Cu₃O_x (YBCO) films grown on polycrystalline Y_0.15Zr_0.85O_1.925/CeO₂/Y₂O₃/Ni₉₅W₅(Ni) rolling-assisted, biaxially textured substrates (RABiTS). A novel analysis technique is introduced in which the orientation of mosaic films is measured by using a Hough transform to recognize arcs in Laue microdiffraction patterns that correspond to low-index zone axes. While the overall epitaxy is cube-on-cube, grain-by-grain analysis reveals a systematic misorientation of YBCO with respect to Ni: the YBCO (001) rotates toward the direction of the surface normal. The crystal mosaic (for rotation about the rolling direction) measured by a single diffraction pattern sampling a 0.5-(micro)m2 surface area is 0.7 degrees full width at half-maximum for YBCO grown on Ni grains with a low tilt; for more highly tilted grains, the YBCO patterns can no longer be measured, presumably due to the large mosaic. The YBCO mosaic over the entire area of a Ni grain is ∼2.5 degrees and varies with grain size; the mosaic is smaller for larger grains