Within the framework of fully relativistic approaches to describe multielectronic systems, the anapole moment’s enhancement in the cation was calculated ²⁹Si¹⁶O⁺, equal to Wₐ = 14.4 Hz, the error does not exceed 3%. The obtained value can be used in interpreting the results of experiments by measurement of the anapole moment in the indicated cation. Some spectroscopic constants for the X²Σ⁺₁⁄₂, A²Π₁⁄₂, A²Π₃⁄₂ and B²Σ⁺₁⁄₂ states have also been clarified at the level of quadruple excitations, necessary for setting up experiments on laser cooling of this molecule.