<?php
//Do NOT include the opening php tag

//Product search by SKU
function xr_join_product_search( $join, $query ) {
  if ( ! $query->is_main_query() || is_admin() || ! is_search() || ! is_woocommerce() ) {
    return $join;
  }
  global $wpdb;
  $join .= " LEFT JOIN {$wpdb->postmeta} post_meta ON {$wpdb->posts}.ID = post_meta.post_id ";
  return $join;
}
add_filter( 'posts_join', 'xr_join_product_search', 10, 2 );

function xr_where_product_search( $where, $query ) {
  if ( ! $query->is_main_query() || is_admin() || ! is_search() || ! is_woocommerce() ) {
    return $where;
  }
  global $wpdb;
  $where = preg_replace(
    "/\(\s*{$wpdb->posts}.post_title\s+LIKE\s*(\'[^\']+\')\s*\)/",
    "({$wpdb->posts}.post_title LIKE $1) OR (post_meta.meta_key = '_sku' AND post_meta.meta_value LIKE $1)", $where
  );
  return $where;
}
add_filter( 'posts_where', 'xr_where_product_search', 10, 2 );