Can I setup an IVR to route calls in Freshdesk?

Yes, we do have an option to setup an IVR. The IVR in our phone channel is multifaceted and allows you to use the keypress option to route calls to a group, agent or call a number directly. There is an additional feature which lets you jump menus where you could create another IVR and jump to that when you are on the first one. 

Say, for example, you have two departments which need separate IVRs - you could ask the customer to jump to the department they would want to reach. This can be done under Admin-> Phone-> Edit-> Greetings section.