JDBC is rarely used in Android apps, for many reasons. MySQL can, in principle, be made to work in an app, and there are other posts on SO that explain the steps needed to make it work.
But...
In the end, JDBC is an interface to database wire protocols, that are rarely suitable for the kind of networking used in mobile computing. The usual way to do database operations in an Android app is to expose them as webservices on some server that has a strong network connection to the database. The webservice would do the low-level data manipulation, perhaps using JDBC, while accepting and presenting data in a form that is suitable for handling in an app. There are many Java libraries for simplifying the work of acting as a webservice client.
In fact, this approach is almost always used for wide-area access to databases in all contexts, not just Android apps. Most organizations will not expose database wire protocols to the public Internet, because these protocols are hard to route, and it's hard to do it securely.
In short, unless your database server is accessible to your mobile device over a WiFi connection, direct JDBC connection is unlikely to work well, even if the Android-specific problems can be overcome. It's almost not worth trying to overcome these problems, because JDBC is unlikely to be robust, secure, or bandwidth-efficient even if it actually works.