How to find if the website was designed by responsive web design or not?Is there any tool or shortcut ways to find that?

The use of @media queries in the html head would be a strong indicator and quick to check. Look for css files with names that suggest different sizes e.g. mobile.css
<link href="mobile.css" type="text/css" media="screen and (max-device-width: 480px)" rel="stylesheet"/>
CSS links like the one above only run if the media criteria is true so if you see something like this then you have a responsive design.

Or there are some online tools, like this one

Thanks maxweb for provide useful tool.