Considering that we're dealing with a verse from Song of Songs, which is a book of the Bible, it shouldn't surprise us that, accurate or not, the phrase gets used quite a bit. I didn't expect that searching for "voice of the turtle" crossed with, for instance "Ariel and Chana Bloch" would bring me to their translation - though it might perhaps have shown up as part of a comparison of other versions/translations. But there was no reason not to try, and I was already curious - who might be using the phrase. It turned out that quite a few people were.
I was pleasantly reminded, for instance, that a great acoustic guitarist of the '60s whom I enjoyed listening to back then, John Fahey, had released an album in 1968 with the apparently intentional reference to Song of Songs in the title: Voice of the Turtle. I hadn't heard Fahey in years, and stumbling onto the album raised the obvious question of "whatever happened to him?". So, a side-trip to Wikipedia was a good way to catch up with him - and to learn that he'd died in 2001. I doubt his music is heard very often today, though it certainly can serendipitously happen.
Still along musical lines, Voice of the Turtle is the name of a long-standing musical ensemble devoted to Sephardic music. The members of Voice of the Turtle knew quite well that the turtle in their name actually referred to a bird, but still found meaning in the name. From their website:
The "Turtle" is actually a turtledove--the symbol of exile, the harbinger of spring and of peace. It is familiar to English speakers as a "turtle" from the King James Bible. (The Hebrew word is tor. Whether a mistranslation, or simply the poetic form of the word, the "turtle" is able to encompass a vast array of images. Our logo--an ancient lyre with a tortoise shell as its resonating box--is decorated by the Star of David and the Islamic crescent, both ancient symbols. Their juxtaposition evokes a significant part of Sephardic history.The group has recorded numerous albums and performs to critical acclaim.