Even then, any small stretches of DNA that make it past the gut into the bloodstream are ineffective. DNA has to reside in a cell’s nucleus in order to have an effect. Viruses do this: they consist of highly organized bundles of DNA which include things like augur-shaped bits that allow the virus to get inside a cell, where it hijacks the cell’s machinery to step aside from its ordinary function and simply churn out millions of copies of the virus. It isn’t pretty.
The only DNA you need to worry about is a virus; DNA from snake meat, for instance, doesn’t make you grow fangs.