Version an API in Azure API Management using Azure Resource Manager

When creating a new API in an Azure API Management Service using the portal, you can specify whether you would like the API to be versioned

To achieve this through ARM scripts you'll need to create an ApiVersionSet resource first:

{
    "name": "[concat(variables('ManagementServiceName'), '/', variables('VersionSetName'))]",
    "type": "Microsoft.ApiManagement/service/api-version-sets",
    "apiVersion": "2017-03-01",
    "properties": {
        "description": "Api Description",
        "displayName": "Api Name",
        "versioningScheme": "Segment"
    }
}

Then update the apiVersionSetId property on the Microsoft.ApiManagement/service/apis resource:

{
        "type": "Microsoft.ApiManagement/service/apis",
        "name": "[concat(variables('ManagementServiceName'), '/', variables('ApiName'))]",
        "apiVersion": "2017-03-01",
        "dependsOn": [
            "[resourceId('Microsoft.ApiManagement/service/api-version-sets', variables('ManagementServiceName'), variables('VersionSetName'))]"
        ],
        "properties": {
            "displayName": "string",
            "apiRevision": "1",
            "description": "",
            "serviceUrl": "string",
            "path": "string",
            "protocols": [
                "https"
            ],
            "isCurrent": true,
            "apiVersion": "v1",
            "apiVersionName": "v1",
            "apiVersionDescription": "string",
            "apiVersionSetId": "[concat('/api-version-sets', variables('VersionSetName'))]"
        }
    }