I'm not able to tell you why it is that way, but idioma (as well as the similar sounding idiota, and the similarly ending bioma) is a masculine word, so it'd be "el idioma". I wish it were easier to rationalize.
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1. This is the case with many nouns that violate the expectation that an ending in -a would be feminine. The usual chapter one vocabulary word, nauta also comes from Greek, although in that case, the original word is ναύτης which is first-declension in Greek and remains first-declension in Latin, unlike idioma/ἰδίωμα.