
Microsoft just updated it's beta version of Cortana (1.0.0.204). This update will allow users to replace Google Now on their Android home button (either by pressing and holding or dragging up) with Cortana. This will no doubt help make Cortana better integrated with the Android operating system, but even then there are some limitations.

For example Google Now can be activated by saying “OK Google”, but voice activation for Cortana is not possible at the moment due to hardware limitations. This prevents Cortana from constantly listening for its activation phrase, but we reckon this is good enough.
Microsoft hasn’t mentioned when the official version of the app will be available, but one could expect it to arrive shortly. Once the official app is released, all of the features you get with Windows Phone will be available for Android users to enjoy.
Unofficial Microsoft News