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Many borate crystals feature nonlinear optical properties that allow for efficient frequency conversion of common lasers down into the ultraviolet spectrum. Twinning may degrade crystal quality and affect nonlinear optical properties, in particular if crystals are composed of twin domains with opposing polarities. Here, we use measurements of optical activity to demonstrate the existence of inversion twins within single crystals of YAl3(BO3)4 (YAB) and K2Al2B2O7 (KABO). We determine the optical rotatory dispersion of YAB and KABO throughout the visible spectrum using a spectrophotometer with rotatable polarizers. Space-resolved measurements of the optical rotation can be related to the twin structure and give estimates on the extent of twinning. The reported dispersion relations for the rotatory power of YAB and KABO may be used to assess crystal quality and to select twin-free specimens.