WordPress is not designed with a global include setting at the top of the page within the <body>, but GTM can be either be auto-installed in the footer, or by editing the header.php template file.
You need to add the GTM-xxxx ID, into WordPress plugin to activate GTM.
1) DuracellTomi’s Google Tag Manager [Recommended option]
- comment events
- remarketing tags
- native scroll tracking
- weather tracking
- enhanced tag security using blacklisting settings
- works with WooCommerce & ContactForm7
(19,714 downloads, Last Updated 1 week ago on 17th Dec 2014)
2) WP Google Tag Manager
(7,086 downloads, Last Updated 1.9 year ago: 10th January 2013)
3) Metronet Tag Manager
- custom dataLayer via server-side commands.
(1,905 downloads, Last Updated 2 week ago: 11th Dec 2014)
Also worth mention this WooCommerce non-GTM plugin: