It seems that US law does have human biology baked into personhood. I believe some countries have granted or have actual movements for some human rights to extend to non human species (ie primates).
As for the politics of what happens next:
If someone did create a sentient AI like Data from Star Trek it would likely face an immense uphill battle to have any recognized rights, beyond being the property of the creators.
If thus AI did not have a body and charm, the battle for legal recognition would be even starker.
People fear skynet. People fear recognizing the intelligence of animals. I don't think the wheels of public opinion or law would adapt quickly to any new information about a truly human like artificial intelligence.