Using Microsoft WebDeploy with NUKE build, see https://blog.dangl.me/archive/using-webdeploy-via-nuke-build-scripts/

Build.cs

class Build : NukeBuild
{
    [Parameter] readonly string Environment;
    [Parameter] readonly string WebDeployUsername;
    [Parameter] readonly string WebDeployPassword;
    [Parameter] readonly string WebDeployPublishUrl;
    [Parameter] readonly string WebDeploySiteName;

    Target Publish => _ => _
            .Requires(() => Environment)
            .DependsOn(FrontendRestore)
            .DependsOn(BackendRestore)
            .DependsOn(FrontendCompile)
            .Executes(() =>
            {
                DotNetPublish(p =>
                {
                    return p.SetWorkingDirectory(SourceDirectory / "project_name")
                            .SetConfiguration(Environment)
                            .SetOutput(OutputDirectory);
                });
            });

    Target Deploy => _ => _
        .DependsOn(Publish)
        .Requires(() => WebDeployUsername)
        .Requires(() => WebDeployPassword)
        .Requires(() => WebDeployPublishUrl)
        .Requires(() => WebDeploySiteName)
        .Executes(() =>
        {
            WebDeploy(s =>
            {
                return s.SetSourcePath(OutputDirectory)
                        .SetUsername(WebDeployUsername)
                        .SetPassword(WebDeployPassword)
                        .SetEnableAppOfflineRule(true)
                        .SetPublishUrl(WebDeployPublishUrl)
                        .SetSiteName(WebDeploySiteName);
            });
        });
}

jenkins.ps1

./build.ps1 -target Deploy `
    -Environment 'Staging' `
    -WebDeployUsername '$appname' `
    -WebDeployPassword 'password' `
    -WebDeployPublishUrl 'https://appname.scm.azurewebsites.net:443/msdeploy.axd?site=appname' `
    -WebDeploySiteName 'appname'