I want to rotate the whole /var/log folder on my server every day so I have the /var/log folder and compressed files like "log.1.gz" which contains the whole directory.
I can't found anything on the man page which can do that.
That is not a good idea. Big part of the log rotation process is forcing applications to change the log file they are using. You to do that for a directory, you need to manage this for all the logs in it.