As specified by Microsoft, to use Cortana on Xbox One you either need to have a Kinect or a headset microphone.

As much as I love my Kinect, it can be expensive to purchase as a standalone device, especially if you have no intentions of using its motion tracking features. Since the new Xbox One S comes with an IR blaster built in, you may find yourself even less likely to want a Kinect unit. Additionally, if you have invested in a dedicated sound system, donning to a headset just for Cortana might seem a little counter-intuitive and silly.

But if you have the revised Xbox One controller with a built-in 3.5mm headset jack, there's an easy, cheap and cheerful method for activating Cortana voice commands on Xbox One.

Amazon is crammed with mini-microphones designed for use on smartphones with dictation software. Thanks to the standardized 3.5mm jack, the Xbox One will detect these discrete mics as a headset. Attaching them to your controller will allow you to activate Cortana commands without purchasing a Kinect or dedicated headphones.

Here are a couple of 3.5mm microphones that should work on your Xbox controller, but if you search Amazon for "3.5mm smartphone microphone" there will be dozens of options. And don't forget to check out our comprehensive Cortana guide!

Thanks Adam for the tip!