For anyone wanting to do this using a powershell
script that calls the KUDU
API and is executed by Octopus deploy
you can follow the steps in my answer here (You can also refer to other answers on this question for some interesting approaches)
Here is the relevant portion for deploying only one function to a function app.
Get your publish profile username and password as described here
$creds = Invoke-AzureRmResourceAction -ResourceGroupName YourResourceGroup -ResourceType Microsoft.Web/sites/config -ResourceName YourWebApp/publishingcredentials -Action list -ApiVersion 2015-08-01 -Force
$username = $creds.Properties.PublishingUserName
$password = $creds.Properties.PublishingPassword
Invoke the Kudu REST API to push your function to the function app
$username = '<publish username>' #IMPORTANT: use single quotes as username may contain $
$password = "<publish password>"
$base64AuthInfo = [Convert]::ToBase64String([Text.Encoding]::ASCII.GetBytes(("{0}:{1}" -f $username,$password)))
$apiUrl = "https://<yourFunctionApp>.scm.azurewebsites.net/api/zip/site/wwwroot"
$filePath = "<yourFunctionName>.zip"
Invoke-RestMethod -Uri $apiUrl -Headers @{Authorization=("Basic {0}" -f $base64AuthInfo)} -Method PUT -InFile $filePath -ContentType "multipart/form-data"