Both expressions appear to have currency according to a very quick look through the Google periscope. The Ngram chart shows an interesting result, suggesting that scared of emerged in the mid to late 19th C., which is contemporary with examples offered up by couple of online dictionaries: Mark Twain's Adventures of Tom Sawyer. It's not quite a "smoking pen", but it's interesting all the same.
Scared by has a robust earlier history, but seems to have lost preeminence, at least in the unblinking eyes of Ngram, to Scared of.
The usual lexicons will define "scared," but seem mum on the subject of trailing prepositions.
Which brings us to the tags "American English" and "Colloquialism" - i.e. the world of anecdote and opinion.
A flight through today's Googleverse shows that people are scared of Donald Trump's candidacy, self-driving cars, and losing the fight with cancer. (Arachnophobes had better move over - it's a scary world out there.) Similarly, people in G-space have been scared by things: intruders, pit bulls and kids in Halloween costumes (well, sorta).
It's an observation backed by lifetime personal usage that one may be scared of things in the abstract, in the future, or on general principles, while scared by seems to denote an experience that is more immediate, proximate, and fang-baringly perilous.
Interestingly, more people seem scared of things than by them, at least if we bet the farm on Ngrams.
The two phrases aren't quite interchangeable, although they seem to be interchanged with a measure of indifferent impunity in the US, where most speakers are not scared of or by grammar books, rules, or curmudgeons who wield them.
