What is (roughly) the net charge of the DNA in an average human cell?
That reasoning seems to work for Harvard's bionumbers database. They use a charge of -2 per base pair, and then estimate the linear charge density as 2e / 0.34 nm, where 0.34 nm is the length of a base pair. There are approximately 3.08 billion base pairs in the human genome, so you could run the same calculation: $2e \cdot 3.08 \cdot 10^9 = 9.86 \cdot 10^{-10} C$.