Every Time Lord we've ever seen has apparently been a member of the Gallifreyan species (and born and raised on Gallifrey). They sometimes talk about Time Lords as a race. And it seems like you have to go through the Academy to become a Time Lord, and you probably can't do that unless you've done all the precursor stuff, like looking into the untempered schism, at a young age.
But that's a whole lot of "apparently" and "seems like" and "probably". There's certainly nothing in the show's history that would prevent a future writer from deciding that a human can become a Time Lord.
In fact, the writers were planning to do that after season 26—the Doctor was going to enrol Ace at his Academy to study to become a Time Lord, and then go off with a new companion. Maybe this would have been an unprecedented thing and the Doctor would have to do something to force them to accept her, or maybe it would have been treated as something uncommon but not unheard of. At any rate, since the show was canceled, that story never happened.
There are many hints, both in the classic series and the new series, that humans will eventually become Time Lords. For example, we're told that the Gallifreyans became Time Lords because of exposure to the time vortex, and River Song is "half Time Lord" despite her normal human parents just because she was conceived in a TARDIS in flight. But then even if we were sure that the human race could one day evolve into Time Lords, that wouldn't tell us that a normal human being like Ace or Jack Harkness could become a Time Lord.
The TV movie tells us that the Doctor himself is half-human on his mother's side. That doesn't tell us his mother became a Time Lord, but it does at least tell us that a half-human can become a Time Lord. Of course many fans turn to the novels and audios to explain away that line and insist that the Doctor is pure Gallifreyan—but if you do that, you're opening a lot of other doors, including Leela and Andred's half-human son becoming a Time Lord.
So, as said at the top, nobody knows. Maybe some future writer will firmly establish the answer one way or the other, but for now, all we have is ambiguous hints and clues that leave the question open.