IdHttp Just Get Response Code

TIdHTTP.Head() is the best option.

However, as an alternative, in the latest version, you can call TIdHTTP.Get() with a nil destination TStream, or a TIdEventStream with no event handlers assigned, and TIdHTTP will still read the server's data but not store it anywhere.

Either way, also keep in mind that if the server sends back a failure response code, TIdHTTP will raise an exception (unless you use the AIgnoreReplies parameter to specify specific response code values you are interested in ignoring), so you should account for that as well, eg:

procedure Button1Click(Sender: TObject);
var
  http : TIdHttp;
  url : string;
  code : integer;
begin
  url := 'http://www.WEBSITE.com';
  http := TIdHTTP.Create(nil);
  try
    try
      http.Head(url);
      code := http.ResponseCode;
    except
      on E: EIdHTTPProtocolException do
        code := http.ResponseCode; // or: code := E.ErrorCode;
    end;
    ShowMessage(IntToStr(code));
  finally
    http.Free;
  end;
end; 

procedure Button2Click(Sender: TObject);
var
  http : TIdHttp;
  url : string;
  code : integer;
begin
  url := 'http://www.WEBSITE.com';
  http := TIdHTTP.Create(nil);
  try
    try
      http.Get(url, nil);
      code := http.ResponseCode;
    except
      on E: EIdHTTPProtocolException do
        code := http.ResponseCode; // or: code := E.ErrorCode;
    end;
    ShowMessage(IntToStr(code));
  finally
    http.Free;
  end;
end;

UPDATE: to avoid the EIdHTTPProtocolException being raised on failures, you can enable the hoNoProtocolErrorException flag in the TIdHTTP.HTTPOptions property:

procedure Button1Click(Sender: TObject);
var
  http : TIdHttp;
  url : string;
  code : integer;
begin
  url := 'http://www.WEBSITE.com';
  http := TIdHTTP.Create(nil);
  try
    http.HTTPOptions := http.HTTPOptions + [hoNoProtocolErrorException];
    http.Head(url);
    code := http.ResponseCode;
    ShowMessage(IntToStr(code));
  finally
    http.Free;
  end;
end; 

procedure Button2Click(Sender: TObject);
var
  http : TIdHttp;
  url : string;
  code : integer;
begin
  url := 'http://www.WEBSITE.com';
  http := TIdHTTP.Create(nil);
  try
    http.HTTPOptions := http.HTTPOptions + [hoNoProtocolErrorException];
    http.Get(url, nil);
    code := http.ResponseCode;
    ShowMessage(IntToStr(code));
  finally
    http.Free;
  end;
end;

Try with http.head() instead of http.get().