MySQL join query using like?

Try

SELECT *
FROM Table1
INNER JOIN Table2 ON Table1.col LIKE CONCAT('%', Table2.col, '%')

MySQL does string concatenation differently from other databases, so in case you want to port your app, you need to have an alternate version where || is used as concatenation operator, as mentioned by Michael in another answer. This operator doesn’t work in MySQL though, since it means or.