It depends exactly what you're defining as "ASCII", but I would suggest trying a variant of a query like this:
SELECT * FROM tableName WHERE columnToCheck NOT REGEXP '[A-Za-z0-9]';
That query will return all rows where columnToCheck contains any non-alphanumeric characters. If you have other characters that are acceptable, add them to the character class in the regular expression. For example, if periods, commas, and hyphens are OK, change the query to:
SELECT * FROM tableName WHERE columnToCheck NOT REGEXP '[A-Za-z0-9.,-]';
The most relevant page of the MySQL documentation is probably 12.5.2 Regular Expressions.