Azure Managed Cache is in preview and hence REST API are not available for it. Also it can not be created from Portal. However, you can use Powershell commands to create it. Once created you can then manage it from azure portal itself.
Following command can be used for creating Basic Cache of 128MB.
New-AzureManagedCache -Name YourCacheName -Location "YourLocation"
For the detailed steps refer to - Create Azure Managed Cache from Powershell
So you can create .ps1 file or powersehll commands string which then can be invoked from your code.
Hope this helps.