Scanning X-ray nanodiffraction on a highly periodic ferroelectric domain pattern of a strained K_0.75Na_0.25NbO₃ epitaxial layer has been performed by using a focused X-ray beam of about 100 nm probe size. A 90°-rotated domain variant which is aligned along [1{\overline 1}2]_TSO has been found in addition to the predominant domain variant where the domains are aligned along the [{\overline 1}12]_TSO direction of the underlying (110) TbScO₃ (TSO) orthorhombic substrate. Owing to the larger elastic strain energy density, the 90°-rotated domains appear with significantly reduced probability. Furthermore, the 90°-rotated variant shows a larger vertical lattice spacing than the 0°-rotated domain variant. Calculations based on linear elasticity theory substantiate that this difference is caused by the elastic anisotropy of the K_0.75Na_0.25NbO₃ epitaxial layer.