You'll need to add the following intent-filters to your activity in the manifest:
<intent-filter>
<action android:name="android.intent.action.VIEW" />
<category android:name="android.intent.category.DEFAULT" />
<data android:scheme="content"/>
<data android:scheme="file"/>
<data android:mimeType="audio/*"/>
</intent-filter>
If you want your app to show up only for mp3 files, try this:
<intent-filter>
<action android:name="android.intent.action.VIEW" />
<category android:name="android.intent.category.DEFAULT" />
<data android:mimeType="audio/mp3" />
<data android:pathPattern="*.mp3" />
</intent-filter>
To read more on intent filters: Link.