Is it possible to use chemecal sterilization for a cat ?
In general this is not permitted. Sterilization of animals is a full Torah prohibition (certainly for males, and possibly even for females), so that we do not permit this even when done by an indirect means of chemical ingestion.
However, because it is an indirect means of sterilization, it is permitted to use chemical methods where there is a significant need, in particular where this is required for the well-being of the cat itself.
See Shulchan Aruch, Even Ha’ezer 5:11 (some maintain that sterilization of a female is only a rabbnic prohibition); Rabbi Moshe Feinstein, Iggros Moshe, Even Ha’ezer IV, 34; For an overview of the issue, see Rabbi Joseph Ozarowski, “Tubal Ligation and Jewish Law: An overview,” Journal of Halacha and Contemporary Society VII, pp. 42-52.
For modern methods of potentially permitted sterilization, see McRae, G.I., et.al. “Long-term Reversible Suppression of Estrus in Bitches with Nafarelin Acetate, a Potent LHRH agonist,” Journal of Reproductive Fertility,(1985) 74 389-397; and Olson, P.N., et.al. “A Need for Sterilization, Contraception, and Obortifacients: Unwanted Pets Part IV. Potential Methods of Controlling Reproduction,” Compendium of Continuing Education, Vol. 8, No. 5, May 1986, 303-307.