Do I have any chance to acquire funding for a PhD after admission? I've just received this email from a university in the US:

" Hello Ernesto,
Thank you for applying to our program! We have received your application and you are a strong candidate.  Do you require funding?
We are happy to accept you if you do not require funding, but we do not have a GA position for you.
 Please let me know your needs and if you have any other questions.
 Sincerely,"

I don't know how to reply them to have any chance to acquire funding; Indeed, scholarships and funds are necessary for my academic life.
They cannot fund you directly, so you need to bring money from elsewhere. Your best bet is to ask them, as they would be aware of the possible agencies that provide grants in your field. They should also be able to help you put together a stronger application.

In any case, your position is uncertain, so don't overcommit to this place, and keep applying elsewhere.