How to programmatically add a 'shortcut' to my app from users' Facebook profiles?

I'd like an icon and label to appear in the section marked in red below, that links to my application canvas 开发者_开发百科page:

Is this possible using any of the current Facebook APIs? No legacy APIs as this is a new app.

No this is no longer possible; the ability to add Apps to profile tabs was announced as deprecated in August 2010 and removed entirely in November 2010. (ref https://developers.facebook.com/blog/post/415/ )

The bookmarks section (visible in approximately the same place you've highlighted, but on the Home / News Feed page rather than the profile) is automatically populated and will have an entry there for your app once users authorise it; this links back to your canvas page or to your bookmark URL if you have one defined