Assign category using custom field?

You should hook into save_post and set the categories using wp_set_object_terms():

// Add an action to run on post save
add_action( 'save_post', 'set_genre_on_save' );
function set_genre_on_save( $post_id ){
    // Check the post type
    if (is_single('tvseries')) {
        // Get the custom field data
        $custom_field_data = get_post_custom( $post_id );
        // Check if there is any genres entered in the metabox
        if (isset($custom_box_data['genre'])) {
            // Save the genre data (separated by comma) into an array
            $genre_array = explode( ',', $custom_box_data['genre'] );
            //Set the array values to lower case
            foreach ($genre_array as $genre){
                $genre = strtolower($genre);
            }
            // Set the categories for these genres
            wp_set_object_terms( $post_id, $genre_array, 'category' );
        }
    }
}

You should enter the slug or the ID of your categories in the field. for example, War Movies won’t work, but war-movies will work. Also there should be no white space between the values (or you have to change ',' to ' ,').

Note that this is just an example, since you didn’t post any code. You might need to change some of the values such as genres to match your custom fields / post types.