Were there any ancient rationalists?

It was a time before LSTMs or Transformers, a time before Pearlian Causal Graphs, a time before computers.

Indeed, it was even a time before Frege or Bayes. It was a time and place where even arabic numerals had not yet memetically infected the minds of people to grant them the powers of swift and easy mental arithmetic, and where non-syllabic alphabets (with distinct consonants and vowels) were still kinda new...

...in that time, someone managed to get credit for inventing the formalization of the syllogism! And he had a whole school for people to get naked and talk philosophy with each other. And he took the raw material of a simple human boy, and programmed that child into a world conquering machine whose great act of horror was to sack Thebes. (It is remarkable how many philosophers are "causally upstream, though a step or two removed" from giant piles of skulls. Hopefully, the "violent tragedy part" can be avoided this time around.)

Libertinism, logic, politics, and hypergraphia were his tools. His name was Aristotle. (Weirdly, way more people name their own children after the person-shaped-machine who was programmed to conquer the world, rather than the person-shaped programmer. All those Alexes and Alexandras, and only a very few Aristotles.)

A lot of this depends on where you draw the line between 'rationality' and 'science' or 'economics' and 'philosophy' or so on. As well, given that 'rationality' is doing the best you can given the constraints you're under, it seems likely that many historical figures were 'rational' even if they weren't clear precursors to the modern rationalist cluster.

For example, I think Xunzi (~3rd century BCE) definitely counts; check out Undoing Fixation in particular. [His students Li Si and Han Fei are also interesting in this regard, but I haven't found something by them yet that makes them clearly stand out as rationalists. Also, like JenniferRM points out, they had a troubled legacy somewhat similar to Alexander's.]

Some people count Mozi as the 'first effective altruist' in a way that seems similar.

People point to Francis Bacon as the originator of empiricism; you can read his main work here on LW [LW · GW]. While influential in English-language thought, I think he is anticipated by al-Haytham and Ibn Sina.

LaPlace is primarily famous as a mathematician and scientist, but I think he was important in the development of math underpinning modern rationality, and likely counts.

Benjamin Franklin seems relevant in a handful of ways; his autobiography is probably the best place to start reading.

Alfred Korzybski is almost exactly a hundred years older than Yudkowsky, and is the closest I'm aware of to rationality-as-it-is-now. You can see a discussion of sources between then and now in Rationalism Before The Sequences [LW · GW].

May be the most surprising answer will be Paul Valéry. He is a great poet but during one night in 1892 he decided to spend all his life in solving the mystery of intelligence and wrote extensive notebooks about it. https://collecties.kb.nl/en/koopman-collection/1951-1960/cahiers