Just keep a few things in mind before you download the Cortana for Android APK. Remember that it is not a finished product, so don't expect it to be perfect. Cortana for Android will be available at first only in China and the U.S. Microsoft says that it will roll it out to more countries as time goes by. To load the APK, you first need to enable the "Unknown sources" setting by going to Settings > Security. Enabling the feature will allow you to install apps from unknown sources. To load the APK, click on the sourcelink. The file weighs in at 19.1MB.
Right now, saying "Hey Cortana" won't wake up the ol' gal on Android, but Microsoft is working hard on bringing over as many of Cortana's features to Android as possible. This, however, is going to take some time.
source: com.microsoft.cortana.apk vi, Microsoft via RedmondPie