//You need to be running java 7 I believe!
String ip; //where ip will be saved
try {
    BufferedReader in = new BufferedReader(new InputStreamReader(new URL("http://jackhallam.net/checkip.php").openStream()));
    ip = in.readLine().split("<")[0];
    in.close();
}
catch (Exception e) {
    //Handle no ip found
}