Hi Joe,
Couple of options off the top of my head that would allow you to use a non-Azure datacenter IP:
First if you buy/lease a /24 or larger public IP address block you can bring that block into Azure. This is known as "Bring your Own IP addresses" or BYOIP. You would need to buy/lease the block from a third party. Downside is cost and administrative overhead.
Please see article below for more details:
Second would be to route all of your Azure resources' Internet traffic through your on-premises network using Virtual Network Gateway with/without ExpressRoute. In this way the public IP address would be among those that are assigned to your on prem network. Downside is cost, extra latency, less max throughput, administrative overhead, higher risk of network downtime.
Please click Accept Answer if the above was helpful.
Thanks.
-TP