Paul refers to ἀρσενοκοίτης, “sleeping with men”, which is an expression for the concept of homosexuality. Predating the modern term homosexuality. And indeed, which might well be rendered as “homosexuality”, even though it was not the word that Ancient Greeks used. There is a contrary opinion that it refers specifically to temple prostitution in Leviticus; but I find that unconvincing: I have no problem believing that Paul was anti-gay.
See the diversity of opinions in Homosexuality in the New Testament.
So the Greek of the Bible doesn’t use the Modern Latin-derived word homosexuality, just as it doesn’t use the Modern Latin-derived word crucifixion. But it certainly uses a reference to homosexual practices, in a negative sense. And so did Ancient Greeks; kinaideia, for example. (For the difference between negative and positive references to homosexuality, see e.g. Nick Nicholas’ answer to Why were there (apparently) more homosexual men in Ancient Greece than today?)