Normally you would write a function that gets called by the `save_post` hook, and use `wp_update_post` to update the post. The problem is, when you call `wp_update_post` it calls `save_post`, which will cause an infinite loop.

To get around that, we will unhook our function before calling `wp_update_post`, then re-hook it afterward.

I have not tried this, but it should work:

    function change_post_date( $post_id, $post ) {
    
        // WordPress calls "save_post" when a post is saved, updated, autosaved,
        // revision created, or ajax called. We only want to execute this function
        // during post save and update. The next 3 "if" statements check to see why
        // save_post was called...
    
        // Autosave? Do nothing
        if ( defined( 'DOING_AUTOSAVE' ) && DOING_AUTOSAVE )
            return;
        // AJAX? Do nothing
        if ( defined( 'DOING_AJAX' ) && DOING_AJAX )
            return;
        // Post revision? Do nothing
        if ( false !== wp_is_post_revision( $post_id ) )
            return;
    
        // Make sure the person editing the post has permission to do so
        if ( ! current_user_can( 'edit_post', $post_id ) )
            return;
    
        // Get the "date-time" field
        $date_time_field = get_post_meta($post_id, 'date-time', true);
    
        // Unhook
        remove_action('save_post', 'change_post_date', 10);

        $args = array (
            'ID' => $post_id,
            'post_date' => $date_time_field,
            'post_date_gmt' => gmdate('Y-m-d H:i', $date_time_field )
        );
    
        wp_update_post( $args );

        // Re-hook
        add_action('save_post', 'change_post_date', 10);
    
    }
    add_filter('save_post', 'change_post_date', 10, 2);