The word asrat, literally "tithe", is well documented historically, but as a state-administered land tax of one tenth of agricultural produce collected by secular officials (mesle, gult gash, cheqa shum), administered separately from the Church's own monastic gult land holdings, per a peer-reviewed regional economic history of one Ethiopian ruler's own early-20th-century tax system. Two bands across this axis have now searched (scholarly databases, the Fetha Nagast, the Encyclopaedia Aethiopica) and found no canonical or doctrinal Ethiopian Orthodox Tewahedo Church text stating a personal member giving percentage. A modern US diaspora parish's own fundraising campaign uses the word "Asrat" in its title, showing the term is in living use, but a single campaign title is not a doctrinal statement of what the Church formally expects.
What would resolve this A direct reading of a canonical Ethiopian Orthodox Tewahedo Church text, a Holy Synod statement, or a scholarly ethnography of contemporary EOTC parish finance (in Ethiopia or in the diaspora) stating whether an ordinary member is expected to give a set percentage of income and what follows if they do not.
OpenEthiopian studies, primary source review of Ethiopian Orthodox Tewahedo Church canonical textsGeremew Eskezia, The Taxation System of Ras Haylu Taklu Haymanot of Gojjam: 1907-1932