You can add your Site Tracking Code in your Google Tag Manager by following the snapshots below:

tag-manager-main

Click on New Tag:

tag-manager-create

Choose Custom html:

tag-manager-custom

Add your site tracking code:

tag-manager-custom-insert

Select when to fire your New Tag:

tag-manager-triggers

Save your New Tag then click on Verify form your Dashboard to make sure the installation is firing properly.