[dviper]

РЕШЕНИЕ

Код:

procedure TForm2.Button1Click(Sender: TObject);
var
  fStream: TStream;
begin
  fStream := TStream.Create;
  if OpenDialog1.Execute then
  begin
    fStream := TFileStream.Create(OpenDialog1.FileName, fmOpenRead);
    IdWebDAV1.Request.Clear;
    IdWebDAV1.Request.CharSet := 'utf-8';
    IdWebDAV1.Request.BasicAuthentication := False;
    IdWebDAV1.Request.CustomHeaders.Add('Accept: */*');
    IdWebDAV1.Request.CustomHeaders.Add('Authorization: OAuth *******************');
    IdWebDAV1.Request.CustomHeaders.Add('Expect: 100-continue');
    IdWebDAV1.Request.CustomHeaders.Add('Content-Type: application/binary');

    IdWebDAV1.DAVPut('https://webdav.yandex.ru/123.rar' , fStream, '');
    Application.ProcessMessages;


    fStream.Free;
  end;
end;