No, this industry is far from being like the other engineering disciplines. It should be like them, but it is still far too immature to be put at that level.
Licensing would require settling on actually understanding that software development is an engineering activity and not an extended CS 401/501 project. The industry isn't even mature enough to consider licensing either.
In Australia, non-citizens can get engineering licenses. The process is basically the same as a citizen (just more complicated because of visa requirements, as you would expect).
What? Of course non-citizens can get an engineering license. It can be trickier if your education is from outside the US, but citizenship is not an issue.
