In English we say "I speak sign language," I'm curious if the same idiom exists in other languages too or do they refer to it differently?
In the major varieties of Chinese, using the usual words for "speak" (Mandarin: 說/说 shuō or 講/讲 jiǎng; Cantonese: 講 gong2) for sign language would be distinctly odd and non-native. Even on the wild spaces of the Sinophone Internet, it is not attested.
For oral languages using 說 or 講 is standard:
Wǒ tīng bù dǒng, tā zài jiǎng yīngyǔ ma?
I can't understand [him] - is he speaking English?
But actually this is restricted to the literal act of speech in English. The native idiomatic equivalent of the English question "Do you speak English?" is to use a verb relating to "can / to be able to" or "to know" (Mandarin: 會/会 huì; Cantonese: 識 sik1) directly with the object, and this is true of oral and sign languages. Pairing this with 說/講 is nonetheless possible for oral languages.
Rather, the most common verb for "to be signing a sign language" is the equivalent of "to use", Mandarin: 用 yòng, Cantonese also using: 使 sai2.
This means it is identical in form to "to use sign language", and this is especially common as a coverb "to use sign language to..." It is not uncommon to have such collocations as: 用手语说, literally "to use sign language to say".
In French too we'd say « Je parle la langue des signes. », as well as Hungarian „Beszélek jelnyelven.”, I think it's a pretty natural way to describe it, as it is undeniably considered as a language for anybody in the world, and we're used to saying we "speak" languages, so I guess this one doesn't make an exception.
The equivalent of “to speak sign language” exists in all of the Nordic languages, although in my experience people are somewhat more likely to say that they “use” that language.
In Swedish, at least, the phrase “to speak sign language” is commonly encountered both in colloquial speech and in official documents, very often in the sense ‘to know sign language‘. The following is from a report submitted to the Swedish Ministry for Culture in 2017:
Teckenspråkstolkning innebär att en person som talar teckenspråk översätter det talade språket till teckenspråk.
(“In sign language interpretation, a person who knows sign language translates the spoken language into sign language.”)