Yes, there are many projects in GitHub.
They use the collaborative development tools like Git that allow writing and reviewing any complex text. It is normally a text written in a programming language but can be also text of some legal document.
These tools resolve the main problems with the document that is being built by the team:
- If multiple people edit non-overlapping parts of the document, the changes can be merged automatically.
- If two people make changes in the same place, there is a merge conflict that human can still usually resolve.
- If somebody proposes a change, a mature project may want to view the change separately and discuss by community before merging.
- Issues can be raised via issue tracker, assigned, discussed and resolved, rather than people just making random edits.
- If somebody does not like your constitution, can easily fork your project and make the own changes, and the diff of all changes made can be easily displayed.
- Do use the open source license if your goal is to improve the humanity.
Many of the "constitutions" we see on a GitHub search look like some very limited scope projects intended for maybe student groups doing something and wanting a regulatory document for they organization. In some cases the complete constitutions of some countries are present as projects - these are probably not under exactly development.
Main challenge would be to raise a good idea above the swamp of the low quality content so that people would see. Contributing a good, competent draft of some constitution may help. In these days you cannot just setup an empty project and expect people to come.