jdbc:mysql://whatever_publichost_your_db_has.rds.amazonaws.com/db_name?autoReconnect=true&useSSL=true&requireSSL=true
Notice the useSSL and requireSSL as connection parameters
Then you need to import the following SSL certificate into your Java cacerts trusted store:
sudo keytool -import -keystore /PathToYourJDK_OR_JRE_lib/security/cacerts -file path_to_downloaded_from_above_file/mysql-ssl-ca-cert.pem
Set the correct JDBC username/password when connecting and all should be fine.