Use .NET console redirect:
VB.NET Code:
  1. Dim psi = New ProcessStartInfo("curl.exe")
  2. psi.UseShellExecute = False
  3. psi.RedirectStandardOutput = True
  4. psi.Arguments = "ipinfo.io"
  5. Dim p = New Process()
  6. p.StartInfo = psi
  7. p.Start()
  8.  
  9. Dim rdr = p.StandardOutput
  10. Dim output = rdr.ReadToEnd()


Or just use the web API provided by ipinfo.io:
VB.NET Code:
  1. Private Function GetIPInfoFromIpInfoIO() As String
  2.     Using http = New WebClient()
  3.         Return http.DownloadString("http://ipinfo.io")
  4.     End Using
  5. End Function
  6.  
  7. Sub Main()
  8.     Console.WriteLine(GetIPFromIpInfoIO())
  9.  
  10.     Console.WriteLine()
  11.     Console.WriteLine("Press Enter to exit...")
  12.     Console.ReadLine()
  13. End Sub