Based on the Gist by Carl Alexander (https://gist.github.com/carlalexander/4106cfaaf405cec454ba195631bcb6bc), found via http://wordpress.stackexchange.com/a/244992/112824

utf8-to-utf8mb4.php

<?php
/*
Plugin Name: UTF8mb4-convert
Version: 1.0
*/

function update_db_to_utf8mb4() {
    if ( ! isset( $_GET['update-utf8bm4'] ) ) {
        return;
    }

    require_once( ABSPATH . 'wp-admin/includes/upgrade.php' );
    /** WordPress Administration API */
    require_once( ABSPATH . 'wp-admin/includes/admin.php' );
    /** WordPress Schema API */
    require_once( ABSPATH . 'wp-admin/includes/schema.php' );
    global $wpdb;
    if ( is_multisite() ) {
        $tables = $wpdb->tables( 'blog' );
    } else {
        $tables = $wpdb->tables( 'all' );
        if ( ! wp_should_upgrade_global_tables() ) {
            $global_tables = $wpdb->tables( 'global' );
            $tables        = array_diff_assoc( $tables, $global_tables );
        }
    }

    foreach ( $tables as $table ) {
        maybe_convert_table_to_utf8mb4( $table );
    }
}

add_action( 'wp_loaded', 'update_db_to_utf8mb4' );