Probably water hammer, caused by pipes rattling in the wall when the inlet valve closes. Washing machines and dishwashers can also exhibit it. Call a plumber if it's a continuing problem of concern. Damage can occur to plumbing if the rattling and movement is violent enough to cause pipes to loosen.

What is Water Hammer?

Thanks for responding but that can not be the problem. This refrigerator was installed in 2008 and the problem just started a few weeks ago. Thanks again!

It can be a new problem. Years of surges could have progressively loosened pipe anchors in the wall such that the rattle happens now. Or supply mains pressure may have increased. Are you on a municipal supply or private well? Or possibly the refrigerator's inlet valve is worn from years of operation and slamming closed now (they're typically designed to be soft-close to avoid the hammer surging). Good luck solving the mystery.