For many years, various experiments have attempted to shed light on the nature of dark matter (DM). This work investigates the possibility of using CaWO$_4$ crystals for the direct search of spin-dependent DM interactions using the isotope $^{17}$O with a nuclear spin of 5/2. Due to the low natural abundance of 0.038$\%$, an enrichment of the CaWO$_4$ crystals with $^{17}$O is developed during the crystal production process at the Technical University of Munich. Three CaWO$_4$ crystals were enriched, and their $^{17}$O content was measured by nuclear magnetic resonance spectroscopy at the University of Leipzig. This paper presents the concept and first results of the $^{17}$O enrichment and discusses the possibility of using enriched crystals to increase the sensitivity for the spin-dependent DM search with CRESST.