Is there a minimum shiur to be chayav (liable) for anointing on Yom Kippur, and, if so, what is it? The gemarah (Yoma 76b) seems to learn it out as a comparison to food consumption: would that mean it has the same shiurim?
The Mazal Sha'ah on the Rambam infers that the shi'ur l'chayyev for anointing with t'rumah oil is a k'zayis, based on R' Yehudah's opinion in the gemara (K'risus 6b) who holds that a person is liable for a k'zayis of prohibited anointing with the shemen hamishchah (Commentary to Mishneh Torah, Hil. T'rumos 10:2). (One should note that it is still Biblically forbidden to anoint with even less than a k'zayis, at least in the case of the shemen hamishchah).
Although in those cases the oil itself is a prohibited substance, one might consider further extrapolating the above standard to the prohibition against anointing on Yom Kippur. However, disagreement among the Rishonim about the Biblical or rabbinic status of the anointing prohibition on Yom Kippur suggests that there must at least be no Biblical penalty for anointing. Rashi and the Rambam both maintain that the punishment for violation is makas mardus (Rashi on the Rif, Shabbos, Chapter 9; Rambam's Peirush HaMishnayos, Shabbos 9:4, and Tosafos Yom Tov, ibid., who clarifies the Rambam's position). The lack of a Biblical penalty is confirmed by the Yerushalmi (Yoma 8:1; see also Korban HaEidah ibid., s.v. Aval lo l'onesh) Therefore, the issue of a liable quantity seems moot.
Furthermore, a lengthy halachic discussion by Dayan Y.Y. Fisher (Even Yisrael, Hil. Ma'achalos Asuros 17:27) yields the conclusion that, according to those Rishonim who view anointing as Biblically forbidden, the Biblical prohibition against consuming a chatzi shiur of nourishment on Yom Kippur may be derived from the prohibition against anointing (which is itself derived from Daniel, 10:3,12). This seems to be premised on the lack of a minimum shi'ur for anointing on Yom Kippur.
Notably, the Semag distinguishes between Biblically and rabbinically prohibited anointing, though not in terms of the quantity of ointment used. He maintains that a criterion for the Biblical prohibition against anointing on Yom Kippur is anointing the entire body, while anointing even part of the body is forbidden rabbinically (Tosafos Y'shanim, Yoma 77b). This view is echoed by the Mabit (Kiryas Sefer, Hil. Sh'visas Asor, 3).