Funny article. Is it a "Yes"?
So back to our original question: does the Covid-19 vaccine change your DNA? Not directly, no. But yes, thanks to your own immune system, the overall mixture of DNA in your body is a tiny bit altered after you get any vaccine. Your DNA is also changed every time you recover from an infection, including the common cold. But the only change is in the DNA of a tiny number of immune cells, which hang around as guardians against future infections. And that’s a good thing.