Microsoft had first announced in May this year that Cortana will soon be released for the Android and iOS platforms. So far, only the Android version has been released as beta by Microsoft. The iOS version is currently in development but it is unclear when exactly Microsoft will release it.
As you would expect, Cortana on Android isn’t capable of performing all the tasks that it can in its native Windows environment. However, more features will be added as the development proceeds further in the near future.
If you live in the US, you can click on this link and get the Cortana app for Android. The app will be released in other markets as well but no timeframe has been given out just yet.