Can I post a MP3 music file in Facebook?
Follow the instructions in the below links to know more -
The best way to do this in my opinion is to take the file and make it public in your Dropbox, then share a link to the public file as a status.
Dropbox explains how to do this here - just throw the file into your Public folder or make it public and copy the link. Then share and you'd good to go!
How to Add Music to Facebook
How to Put a WAV on Facebook
How to Put a Sound File on Facebook
Grooveshark introduces music sharing plugins for Facebook and WordPress
How to Share a Song From Spotify on Facebook