Is there a way of adding my iCalendar to the native Calendar app of elementary OS? I imagine that I should find a CalDav link for that.
You're right. If you know your CalDav URL, then it's simple to add to Calendar.
In Calendar, you can click on the gear icon, then click Add New Calendar.... For Type, select "CalDav", then enter the CalDave URL along with your username and password. Click Create Calendar and your events should begin syncing.
It took me a while, but I figured it out. elementary's Calendar app does not support the webDav format, which is what is needed. For accessing the iCalendar, you can install the California calendar application which supports the specific format.