The answer to this depends to some degree on how you define a veteran. If you define a veteran as someone who has served in the armed forces, but who is no longer serving, then there were about 22 million veterans in the United States in 2014. In 2014, the population of the United States was about 318.9 million. This means that about 6.9% of Americans were veterans.
If you define veterans to include people who are actually in the military right now, the percentage is a little bit higher. This link tells us that about 1.4 million people are serving in the military right now, which is about .4% of the population. When those people are factored in, we can say that about 7.3% of Americans are serving or have served in the military.