Using Powershell 3, I had the same problem but ended up doing this:

$UnicodeFileName = $ScriptPath + "\UnicodeFileContent.sql"

$FileContent = Get-Content $FileName

$FileContent | Out-File -FilePath $UnicodeFileName -Encoding Unicode

Invoke-Sqlcmd -ServerInstance $SqlServer -Database $Database -InputFile $UnicodeFileName -AbortOnError -Verbose