function TamArquivo(Arquivo: string): Integer;
begin
with TFileStream.Create(Arquivo, fmOpenRead or fmShareExclusive) do
try
Result := Size;
finally
Free;
end;
end;

Solução enviada por Dennis Göhlert (Berlin/German):

function GetFileSize(const szFile: String): Int64;
var
 fFile: THandle;
 wfd: TWIN32FINDDATA;
begin
 result := 0;
 if not FileExists(szFile) then exit;
 fFile := FindFirstfile(pchar(szFile),wfd);
 if fFile = INVALID_HANDLE_VALUE then exit;
 result := (wfd.nFileSizeHigh*(MAXDWORD))+wfd.nFileSizeLow;
 windows.FindClose(fFile);
end;