Take a look at this. Absolutely nothing wrong with being introverted - help them to be comfortable with it. Also, I think everyone feels socially awkward at some time or another. Just make sure they don't feel alone in it.
My son is also an introvert. He comes from a long line of them...
While my son has been described as "quietly confident" and has always been relatively comfortable in his own skin, I did have him read the sister book to the above Ted talk, Quiet by Susan Cain, in 8th grade. He would not be headed to his base high school, with the kids he had been with for the past nine years, but instead be off to a bigger pond where he would know very few. I wanted him to have a deeper understanding of his introversion before he jumped in with a whole new peer group.
As others mentioned above, I also continue to be amazed at how he would dread having to stand on a stage in a theater but is completely unfazed and unflappable on the "stage" of the pitcher's mound...(or batter's box, or anywhere else between the white lines).