According to the features presented on the official website, Calendly is said to be working with the following services: Google, Outlook, Office 365 or iCloud calendar. As you can see, it can be directly integrated into the iCloud which means you can use your iPhone or iPad to access the calendar directly once you've integrated it.
There is also Exchange support through Outlook and a plug-in available from the official website of the developers. They explain the procedure how to connect to Exchange servers if your company uses one.
For additional help, get in touch with them using the available contact details.