Migrations are version control for your db. There is no point in writing migrations if you don't intend to use the version control functionality.
So simply, you can alter the table by creating a new migration... from the command line:
php artisan make:migration alter_table_admin_add_foreign_tag
Then in your new migration, do your up and down methods.
Once your migration is ready,
php artisan migrate.
REGARDING EDITED QUESTION:
Both tables need to be
innodb and not
myisam. Further, both columns parent key and relation key need to be the same data type. As such, in your
tags table is also configured with
$table->char('tag' , 15);
SIDE NOTE / suggestion:
Why do you have some tables singular and some plural. and why do you have some tables starting with a capital letter, and other tables in lower case?
Admin could be
tags could remain
tags for consistency.