The description for the Kenku race (VGtM, p. 109-111) includes this statement:
You can read and write Common and Auran, but you can speak only by using your Mimicry trait.
In the Kenku origin tale, the description further explains that:
[…] to ensure that the kenku could never divulge any secrets, their master took away their voices.
and
Although unable to speak in their own voices, kenku can perfectly mimic any sound they hear, from a halfling's voice to the noise of rocks clattering down a hillside. However, kenku cannot create new sounds and can communicate only by using sounds they have heard. Most kenku use a combination of overheard phrases and sound effects to convey their ideas and thoughts.
Kenku can't speak except by mimicry.
The Kenku have a voice, but it seems they don't have the ability to vocalize their own words; they have no voice of their own. However, they can form their own words because they can write Common and Auran, so they can form their own words in writing (right?). The Mimicry trait is clearly for speaking only.
As sign language is neither vocalized nor written, I would like to know:
Can a Kenku learn sign language and use it to communicate without mimicry?
Best Answer
While Kenku are unable to form voices of their own, there's nothing to stop them from communicating nonverbally. That being said, there's two issues. Part of the Kenku curse is that they lost the creative spark, so any sign language would have to be made for them by someone from another race. Even if a kenku could have a sign language created for them, they'd run into issues that people with real sign language deal with, so some things to consider would be:
Additionally, it bears repeating that "because their ingenuity and skill had turned toward scheming against their patron, the spark of creativity was torn from their souls." A kenku can learn writing by seeing words, but they cannot create words or write words they've never seen. Their vocabularies, both written and spoken, are done by mimicry and copying.