At this point in time, ISE is not supported running natively on any cloud platform.
For the currently latest release (ISE 2.7), Cisco lists the following supported virtual environments:
Cisco ISE supports the following virtual environment platforms:
- VMware ESXi 5. x (5.1 U2 and later support RHEL 7), 6. x
- KVM on RHEL 7.0
- Microsoft Hyper-V on Microsoft Windows Server 2012 R2 and later
If you were doing this on AWS, you could try something like VMware on AWS to run an ESXi hypervisor to run ISE on. With Azure you can try running nested Hyper-V servers, but I wouldn't feel comfortable recommending this.
In a recent fully virtualized AWS deployment, we ended up running ISE on rented co-located servers connected through IPSec VPNs to our AWS environment. Not ideal, but at least it's fully supported.