Check out this youtube video from apollon1965 (who is no doubt Algerian), where he plays one side of an e.p. by an Algerian singer named Karoudji. The first track, "Brigitte Bardot Bardot," is very Cuban in its feel, especially when you get to the piano interlude starting at about 1:15, and it's not really a twist. Karoudji sings it in that distinctive francarabe style developed by Algerian popular musicians beginning in at least the 1930s.
I am unable to make out the title of second track (starting at 2:55) from the record jacket. It opens with a kind of flamenco guitar intro, but then shifts into a cover of Chubby Checker's 1961 hit "Let's Twist Again," which hit #8 on the US charts, and charted throughout Europe as well. "Let's Twist Again" in Algerian Arabic! It's a pretty decent cover too, rockin' sax solo.
According to apollon1965, Karoudj was a singer originally from Oran, who sang rock'n'roll and twist in the early 1960s. I'm not sure whether this was recorded prior to Algerian independence (July 1962) or after.
I've been able to find out nothing else about Karoudj thus far other than the fact that he also recorded a cover of Johnny Hallyday's 1961 single "24,000 Baisers." (It must have been a hit in France, as it was covered by several other artists, among them Dalida and Bob Azzam.) Here's the cover of Karoudji's EP.
According to the writeup by the amourdurocknroll.fr website, Karoudji recorded "24,000 Baisers" in French. The other tracks, "Si Tu Voulais," "Twist à B.B.," "Zinek," "Yasmina," and "Rock's Twist," seem to have been recorded in Arabic. The EP was released in 1963 (after independence) on the La Voix du Globe label, in Oran and Paris.
There is also a film about the twist in Algeria, director Mahmoud Zemmouri's Les Folles Années du twist (The Golden Years of the Twist), released in 1986. I've only seen some clips of it, but it is about two young Algerian men who are obsessed with rock'n'roll and dressing like hip rocksters and are disinterested in either working or the war of liberation. The only information I have about the music in the soundtrack is that it features at least one song by French pop star Richard Anthony, known for covering US rock'n'roll songs in French (as was Johnny Hallyday). Anthony even did a version of "Let's Twist Again," which he recorded in English.
aneéne (about which I've not been able to find anything). He sings it in French, but it has just a bit of Eastern flavor, and he even calls it a "twist Orientale." Music and lyrics were composed by Bentir himself. Perhaps the optimism he expresses is that of his newly independent country. It's recorded with a French group, Jean Claudric et son orchestre, who appeared on numerous French recordings (including some by the Algerian Jew and French pop star Enrico Macias, born Gaston Ghenassia), and it was put out on the El Frida label (which I assume is Algerian). (The song also seems also to have been issued under the name "Manach Dalam (Twist Oriental)" on the Spanish label Vergara.)
The only other track I've been able to find from Bentir is the rock song, "Prête-moi mille balles" (Lend me a thousand bullets), which apparently evokes the Algerian revolution.
Bentir was by all accounts an important figure in this period, but I've not been able to find out much about him, and some of what I've found seems unreliable. For instance, the claim that he placed second in the 1966 Eurovision contest, and although his song was clearly superior, he was denied a victory because he was an Arab. But in fact he was not an entrant in Eurovision, that year or any year. (Algeria does not compete in Eurovision, in any case.)
Last note: I love this EP cover, put out by Philips in France, which was once for sale on-line, but alas, no more.