Can we add border around the fontawesome icon using css?

Yes you can. Use a text-shadow:

.my-icon {
     text-shadow: 0 0 3px #000;
}

Or Also you can use webkit text stroke remember it only work with Chrome and Safari

CSS-Tricks example

-webkit-text-fill-color: white;
-webkit-text-stroke-width: 1px;
-webkit-text-stroke-color: black;