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]

Supports:

comment events
remarketing tags
native scroll tracking
weather tracking
enhanced tag security using blacklisting settings
works with WooCommerce & ContactForm7

http://wordpress.org/plugins/duracelltomi-google-tag-manager/

(19,714 downloads, Last Updated 1 week ago on 17^th Dec 2014)

2) WP Google Tag Manager

http://wordpress.org/plugins/wp-google-tag-manager/stats/

(7,086 downloads, Last Updated 1.9 year ago: 10th January 2013)

3) Metronet Tag Manager

Supports:

custom dataLayer via server-side commands.
http://wordpress.org/plugins/metronet-tag-manager/stats/
(1,905 downloads, Last Updated 2 week ago: 11^th Dec 2014)

Also worth mention this WooCommerce non-GTM plugin:

http://wordpress.org/plugins/enhanced-e-commerce-for-woocommerce-store/

http://www.tatvic.com/enhanced-ecommerce-google-analytics-plugin-woocommerce/