The personal digital assistant - dubbed "M" - completes tasks along with seeking out information at the behest of users.
"Unlike other AI-based services in the market, M can actually complete tasks on your behalf," Facebook's David Marcus said in an online post.
"It can purchase items, get gifts delivered to your loved ones, book restaurants, travel arrangements, appointments and way more."
Marcus described the test as an early step in a journey toward building a large-scale service using the virtual assistant software.
The launch is part of an effort by Microsoft to expand its mobile presence despite a weak showing for its Windows Phone devices.
"The Cortana app can do most of the things Cortana does on your PC or on a Windows phone," Microsoft's Susan Hendrich said in a blog post.
"With the app, you can manage your hectic lifestyle by setting and getting reminders, searching the web on-the-go, tracking important information such as flight details, as well as starting and completing tasks across all of your devices."
A beta version of Cortana was made available on Monday to US users of Android devices, and "we are planning to roll it out to other markets," Hendrich said.