Asana has an API out which they are calling their "REST" api. https://blog.asana.com/2012/04/announcing-the-asana-api/
Some people have made a post-commit script for git which allows you to add a "#task-id" into the message section when you make a commit and that will add a comment into the Asana task which adds your message from the commit and also provides a link to the code file.
Has anyone done this for SVN? I can't seem to find anything online however I thought I would ask first before spending a ton of time trying to make something for SVN and/or trying to learn git and adding their post commit script.