Fact: No. The first COVID-19 vaccines to reach the market are messenger RNA (mRNA) vaccines.
mRNA vaccines teach cells in the body how to make a protein that triggers an immune response. Injecting mRNA into your body will not interact with or change the DNA of your cells. Human cells break down and get rid of the mRNA soon after they have finished using the "instructions."
The mRNA technology behind the new coronavirus vaccines has been in development for almost two decades.