No, it is not possible for you to change your DNA in any way. If it were easy to change a person's DNA, then gene therapy for diseases would be a breeze. As it is, even under the most ideal, lab-controlled situations, it is very difficult to get human cells to incorporate foreign DNA, rather than rejecting it. You would never be able to do it accidentally.
Think of it this way - when a woman is pregnant with a male fetus, there is all sorts of DNA mingling, but nothing ever comes of it.
Hello~As the above poster said, it is not possible to change the DNA in any way.