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;

As of v5.0.6, Font Awesome uses svgs and paths to draw their icons. With a little help from the Inspect Element tool, here's how I put borders around the icon paths.

.fa-comment g g path {
  stroke: black;
  stroke-width: 10;
}

Use text-shadow property like following:

.my-bordered-icon{
  text-shadow: -1px 0 #000, 0 1px #000, 1px 0 #000, 0 -1px #000;
}