This is an except from a short story. Harry is acting for an audition. Doris and the narrator are judging him while acting with him.

(excerpt)
When he faced us again, he was huge and handsome and conceited and cruel. Doris read the part of Stella, the wide, and Harry bullied that old, old lady into believing that she was a sweet, pregnant girl married to a sexy gorilla who was going to beat her brains out. She had me believing it too. And I read the lines of Blanche, her sister in the play, and darned if Harry didn't scare me into thinking like a drunk and faded Southern belle.

(Question): I do not understand "darned if Harry didn't scare me into ---"
Does this just mean "Harry scared me into ----" ?

Yes. The line "darned if Harry didn't scare me into---" is equivalent to "Harry scared me into---"

The term "darned" is a more polite form of "damned." In a Christian society, damned literally means "sent to Hell by God." So if you say "I'll be damned if I do ---," it means that you will not do --- because you don't want to go to Hell. It's a dramatic phrase that can be used as a joke or to express anger. "Damn" is sometimes considered a swear word, so the author used "darn" as a substitute.

The confusing thing about the line you quoted is its use of double negative:
1. "darned if I do ---" or "damned if I do ---" means you do NOT ---. This is a negative.
2. "Harry didn't scare me" or "Harry did not scare me" is also a negative.

So the phrase you questioned is saying that "Harry did not not scare me into---" which means that "Harry scared me into---." For someone whose native language isn't English, your reading comprehension is remarkable! Keep up the good work. :)