How to add a background to a Vector Asset that I want to use as my app's icon?

Since there is no direct way to make a background to a VectorDrawable! So the alternative way is to use a group to arrive to the same Appearance (like a background).

The logic is to make another path before your own vector drawable path so that it may act as a background (No one will notice the difference!) when added together in a group.

For your case this image (with an amber background)!

Was made by adjusting your code like this:

<vector xmlns:android="http://schemas.android.com/apk/res/android"
    android:width="48dp"
    android:height="48dp"
    android:viewportWidth="24.0"
    android:viewportHeight="24.0">
  <group>
    <path android:name="square"
        android:fillColor="#FFFF6F00"
        android:pathData="M0,0 L24,0 L24,24 L0,24 z" />
    <path android:fillColor="#FF000000"
        android:pathData="M12,17c1.1,0 2,-0.9 2,-2s-0.9,-2 -2,-2 -2,0.9 -2,2 0.9,2 2,2zM18,8h-1L17,6c0,-2.76 -2.24,-5 -5,-5S7,3.24 7,6v2L6,8c-1.1,0 -2,0.9 -2,2v10c0,1.1 0.9,2 2,2h12c1.1,0 2,-0.9 2,-2L20,10c0,-1.1 -0.9,-2 -2,-2zM8.9,6c0,-1.71 1.39,-3.1 3.1,-3.1s3.1,1.39 3.1,3.1v2L8.9,8L8.9,6zM18,20L6,20L6,10h12v10z"/>

  </group>
</vector>

So from there you can change the shape (to circular may be) or color (amber to blue) to fit your needs.

After putting a ton of work and research into this, I have finally come up with a solution.

You need three drawables, the background, the vector itself and the drawable that combines the two of them together.

This code gives a brief demonstration:

@drawable/ic_vector.xml:

<vector xmlns:android="http://schemas.android.com/apk/res/android"
    android:width="24dp"
    android:height="24dp"
    android:viewportWidth="24.0"
    android:viewportHeight="24.0">

<group
    android:scaleX="0.8"
    android:scaleY="0.8"
    android:pivotX="12"
    android:pivotY="12">
<path
    android:fillColor="#ffffff"
    android:pathData="M6,18c0,0.55 0.45,1 1,1h1v3.5c0,0.83 0.67,1.5 1.5,1.5s1.5,-0.67 1.5,-1.5L11,19h2v3.5c0,0.83 0.67,1.5 1.5,1.5s1.5,-0.67 1.5,-1.5L16,19h1c0.55,0 1,-0.45 1,-1L18,8L6,8v10zM3.5,8C2.67,8 2,8.67 2,9.5v7c0,0.83 0.67,1.5 1.5,1.5S5,17.33 5,16.5v-7C5,8.67 4.33,8 3.5,8zM20.5,8c-0.83,0 -1.5,0.67 -1.5,1.5v7c0,0.83 0.67,1.5 1.5,1.5s1.5,-0.67 1.5,-1.5v-7c0,-0.83 -0.67,-1.5 -1.5,-1.5zM15.53,2.16l1.3,-1.3c0.2,-0.2 0.2,-0.51 0,-0.71 -0.2,-0.2 -0.51,-0.2 -0.71,0l-1.48,1.48C13.85,1.23 12.95,1 12,1c-0.96,0 -1.86,0.23 -2.66,0.63L7.85,0.15c-0.2,-0.2 -0.51,-0.2 -0.71,0 -0.2,0.2 -0.2,0.51 0,0.71l1.31,1.31C6.97,3.26 6,5.01 6,7h12c0,-1.99 -0.97,-3.75 -2.47,-4.84zM10,5L9,5L9,4h1v1zM15,5h-1L14,4h1v1z"/>
</group>
</vector>

NOTE: The group android:scale tags give padding to your vector.

@drawable/background.xml:

<?xml version="1.0" encoding="utf-8"?>
<shape xmlns:android="http://schemas.android.com/apk/res/android">

<gradient
    android:startColor="#36dad2"
    android:endColor="#5877e6"
    android:angle="45" />

<size
    android:width="25dp"
    android:height="25dp"/>
<corners
    android:radius="5dp"/>


</shape>

And Finally @drawable/icon.xml:

<?xml version="1.0" encoding="utf-8"?>
<layer-list xmlns:android="http://schemas.android.com/apk/res/android">

<item android:drawable="@drawable/background"/>
<item android:drawable="@drawable/ic_android_black_24dp"
    android:gravity="center"/>
</layer-list>

Then Implement icon.xml into your manifest as usual even though you WILL not be able to see a preview of it in manifest.

<?xml version="1.0" encoding="utf-8"?>
<manifest xmlns:android="http://schemas.android.com/apk/res/android"
package="com.dobleu.peek">

<application
    android:allowBackup="true"
    android:icon="@drawable/icon"
    android:label="@string/app_name"
    android:supportsRtl="true"
    android:theme="@style/AppTheme">
    <activity android:name=".MainActivity">
        <intent-filter>
            <action android:name="android.intent.action.MAIN" />

            <category android:name="android.intent.category.LAUNCHER" />
        </intent-filter>
    </activity>
</application>

</manifest>

And Voila! You have a full professional icon.