I could not find any simple Powershell-function to calculate the CRC32 of a given string. Therefore I decided to write my own function which I would like to share in my answer.
Based on the good input from @Cem Polat here a more elegant solution with embededd code:
$crc32 = add-type '
[DllImport("ntdll.dll")]
public static extern uint RtlComputeCrc32(uint dwInitial, byte[] pData, int iLen);
' -Name crc32 -PassThru
$str = "123456789"
$arr = [System.Text.Encoding]::UTF8.GetBytes($str)
$crc = $crc32::RtlComputeCrc32(0, $arr, $arr.Count)
$crc.ToString("X8")