Yes I know the effect you mean – I’ve seen it on desktop recently. However I’m not at a PC at the moment so I’m recalling the visual from memory.
The effect may already have been done on links by other folks. I’ve used something similar for a momentary play/pause indicator here http://fofwebdesign.co.uk/freebies-for-websites/css/slider-rwd-auto-touch-js.htm. Feel free to extrapolate the CSS from that and play around. Else you will need to Google around to find examples to extrapolate from other websites.
If you are unable to create or implement this yourself, and you really want it on your website, it might be an idea to hire someone. Unfortunately, this is not a request forum where you describe what you want and developers come online to do the work for you. Sometimes that may happen, for example, if a developer has already created a demo that they can link you to, or if they take a personal interest and knock-up the whole thing for you free of charge, but it’s not a given. Without sample/starter code of yours to work with, it’s more likely that you’ll get a talk-through of suggested steps and search terms to research online.
At the end of the day, you either do the work yourself (including research and any trial and error learning process to build X effect/module/component) or consider hiring somebody who already has that knowledge.
Good luck with your project.