The mainstream docters like Diederik Gommers from the Netherlands states 3 Januari in the Magazine "Margriet"(Daisy): No, it does not change your DNA... For converting RNA into DNA you need an enzym, reverse-transcriptase, that is only present in some viruses like hepatitis-B or HIV.
Here is the catch
However in the SARS CoV-2/COVID-19 there are 4 HIV1 inserts present. Meaning that the current coronavirus is a retrovirus. Which means that whatever vector is used within mRNA and DNA vaccines results in transfection.