Yes you can. I have applied pink to my natural hair before. What you want to do is go to Sally's Beauty Supply and there is going to be a hair color kit. You must bleach your hair first if you hair color is black, brown, etc.
You can always put hair dye on yourself, if you're daring! However, your best bet, especially risky colors like pink, is to leave it in the hands of a professional stylist. Pink is not an easy color to achieve and can be hard to fix later.