Do you have an API which would allow to share to CB Activity from outside ?

No, API layer is coming with CB 3.x rewrite for CB and for plugins. We'll be utilizing the API, Webservice, and CLI endpoints that Joomla 4 itself provides.

I mean that we have an android/ios application displaying CB activity in a web view and we would like to offer the ability to share external content to CB Activity via the standard iOS sharing buttons

Do you think it possible ?

You should be able to do that using an CB Auto Action as you can create activity through an auto action. Leave Triggers as None and you can call the auto actions URL from an app using an HTTP request. I've no experience with iOS share buttons so beyond that I don't know what to suggest.

The URL for the auto action is provided in the auto action under the Global tab. You'd use that in your HTTP request. You'd still need to know who the user even was though so you'll need to also send their user id with the URL as well.

If you want to create activity then the Mode should be Activity and Method as Create. As for what information you need it depends entirely on what you're even trying to share. If you want to share a URL as an attachment then at the very least you need to send the URL and the users user id to the auto action. Use the parameters in the Links fieldset to attach the URL to the post. It's not really a simply task as again no such API layer exists and you are having to create that entirely yourself.