How to set start page in dotnet core web api?

In Properties/launchSettings.json you can define the launchUrl

"profiles": {
    "IIS Express": {
        "commandName": "IISExpress",
        "launchBrowser": true,
        "launchUrl": "<your relative URL here>",
        "environmentVariables": {
            "ASPNETCORE_ENVIRONMENT": "Development"
        }
    }
}