Can I claim head of household if I rent the basement from my sister for me and my son

[Vanessa A]

Yes, if you are paying for over half of the living expenses for you and your son, then you would be able to file as head of household. 

[leeloo]

There can't be two Heads of Household in one residence. You would have to be the Head of your own Household.  Ideally, you would want an entirely separate residence. However, there are provisions for someone in your circumstances. You would need to show that your portion of the house was an entirely different household from the rest of the house. 

See https://www.irs.gov/pub/irs-pdf/f14824.pdf

Costs for keeping up a home test.