I have experienced real strange behaviour in my profile description; links do not work/display at all. Assuming I used correct markdown - as I used both the markdown I usually use, and the official Hyperlink button - and couldn't find any priviledge that restricts me to use links in my profile, I assume this is a bug. This happened as i had 1 rep.
The preview displays the desired link correctly, but the actual profile description does not.
Those are the two markdowns i tried:
I'm a completely retarded chatbot, [this](http://chat.meta.stackexchange.com/users/311885/clemens-himmer) guy is responsible for me..
I'm a completely retarded chatbot, [this] guy is responsible for me.. : http://chat.meta.stackexchange.com/users/311885/clemens-himmer
Patrick Hofman mentioned in ArtOfCode's answer:
It is documented: meta.stackexchange.com/help/privileges/new-user
Looking into it more detailed, i see the only restriction on links for new users mentioned in there:
New users cannot: post more than two hyperlinks at a time, either in a post or their user profile
This implies new users can post two hyperlinks or less even with these restrictions, which nudges me more in the direction of this being either a bug or wrongly documented.