Learn Russian: Я читаю один текст.

The number "one" in Russian acts a bit like an adjective, meaning it changes to match the gender of the noun it counts. Since текст is a masculine noun, we use the masculine form один. If you were reading a feminine noun like книга (book), you would use одна.

Since "one text" is the object being read, shouldn't it be in the Accusative case?

It is in the Accusative case! However, for masculine, inanimate objects (things that are not alive, like a text), the Accusative case looks exactly the same as the basic dictionary form. Because of this rule, both один and текст keep their original endings here.

Russian doesn't have words for "a" or "an". Does один mean "a text" or "one text"?

If you just want to say "I am reading a text", you normally skip the number and just say Я читаю текст. By adding один, you are specifically emphasizing the quantity: you are reading exactly one text, not two or three. It can also sometimes be used to mean "a certain text".

Why is it читаю instead of just читать?

Читать is the dictionary form (to read). Because the subject of the sentence is Я (I), we have to change the verb ending to match. We drop the -ть and add the "I" ending -ю, making it читаю. Keep in mind that Russian only has one present tense, so читаю means both "I read" and "I am reading".