The Shulhan Aruch (Orah Haim 210:1) writes that the minimum volume required to recite an after-blessing on a beverage is a Revi’it (that is, a Rev’it, or a quarter, of a Log). The Rambam defines a Revi’it as being equivalent to 27 Dirhams, and Rabbi Haim Naeh (Shiure Torah) says that one Dirham is equal to 3.2 cc. According to this reckoning, it follows that a Revi’it is equivalent to 86.4 cc. Interestingly, Rabbi Hadar Margolin and other rabbis explain that archaeological artifacts suggest that the Dirham is actually equivalent to as little as 2.7 or 2.8 cc, and therefore a Revi’it would be closer to 75 cc.
Rabbi Yehezkel Landau (Tziun LeNefesh Haya, Pesachim 109a) argues that the volume of Revi’it used to be larger and that the Revi’it nowadays should actually be double its current amount, which would be at least 150 cc. Rabbi Yedidya Monsenego (Dvar Emet, § 1) argues this opinion and writes that the volume nowadays should actually remain as they are. Rabbi Shalom Messas (Mikraei Kodesh, Pesach) agrees that this is the common practice. Accordingly, a Revi’it is 86 cc., and in light of recent findings, it is as low as 75 cc.
Summary: One may recite a Beracha Aharona after drinking at least 75cc. of liquid.