UpdateVariableValue.ps1

$API_TOKEN = "<replace>" # from https://ci.appveyor.com/api-token
$APPVEYOR_ACCOUNT_NAME = "<replace>" # from AppVeyor project URL
$APPVEYOR_PROJECT_SLUG = "<replace>" # from AppVeyor project URL
$VAR_NAME = "<replace>" # name of variable to update
$VAR_NEW_VALUE =  "<replace>" # new variable value

$API_URL = "https://ci.appveyor.com/api/projects/$env:APPVEYOR_ACCOUNT_NAME/$env:APPVEYOR_PROJECT_SLUG/settings/environment-variables"
$ENCRYPT_URL = "https://ci.appveyor.com/api/account/encrypt"

$headers = @{
  "Authorization" = "Bearer $env:API_TOKEN"
  "Content-type" = "application/json"
}

# get variables collection from server
$s = Invoke-RestMethod -Uri $API_URL -Headers $headers  -Method Get

# check if variable exists
if (($s | ? {$_.name -eq $VAR_NAME}) -eq $null) {
  Write-warning "Cannot find variale $VAR_NAME"
  return
  }

# if variable is encrypted - encrypt new value
if (($s | ? {$_.name -eq $VAR_NAME -and $_.value.isEncrypted -eq "True"}) -ne $null) {
  $body = @{plainValue = $VAR_NEW_VALUE}
  $VAR_NEW_VALUE = Invoke-RestMethod -Uri $ENCRYPT_URL -Headers $headers -Body ($body | ConvertTo-Json) -Method POST
  }

# update variable value
$s | ? {$_.name -eq $VAR_NAME} | % {$_.value.value = $VAR_NEW_VALUE}

# update variables coillection on server
Invoke-RestMethod -Uri $API_URL -Headers $headers  -Body ($s | ConvertTo-Json) -Method Put