You can use register_taxonomy_for_object_type
function and if you say that the taxonomy is created by a plugin you can use the plugins_loaded
hook, to make sure that taxonomy wast already registered so:
add_action('plugins_loaded','add_custom_taxonomy_to_posts');
function add_custom_taxonomy_to_posts(){
register_taxonomy_for_object_type('TAXONOMY_NAME', 'post');
}