Используйте:
$this->execute()
Например:
<?php
use yii\db\Migration;
/**
* Class m180621_120026_install_mgd_old_users_dump
*/
class m185521_188026_install_old_users_dump extends Migration
{
public $maxSqlOutputLength = 100;
/**
* {@inheritdoc}
*/
public function safeUp()
{
$this->execute(
file_get_contents(
__DIR__ . '/dumps/user_dump.sql')
);
}