Crick is a variant of creek originating in the U.S., where it reflects a dialectal pronunciation of the word for a small, shallow stream. Crick might be nonstandard, but it is established enough to be considered an alternative form, and it is even listed in some dictionaries. In writing, crick is often used to create a rustic tone.
Crick appears often in American fiction, especially in first-person narratives and in dialogue—for example:
Just as I was passing a place where a kind of a cowpath crossed the crick, here comes a couple of men tearing up the path as tight as they could foot it. [Adventures of Huckleberry Finn, by Mark Twain]
“… and when night come we taken and throwed their muskets into the crick and taken their ammunition and the rest of the grub and put a gyard on their hosses.” [Flags in the Dust, by William Faulkner]
But crick doesn’t only appear in fiction. Here are a few examples from current news publications and blogs:
Finding a competitive jumping frog could take several trips up and down the crick. [State Journal-Register]
Phlox next, then spring beauties then avalanche lilies, then marsh marigolds up on the edge of the crick where young aspen are budding. [New West (link now dead)]
They find Eric skinny dipping in a nearby crick and taunting gators in Nordic. [Screen Grab]
Of course, if you are not from a part of the U.S. where people say crick, the more standard spelling, creek, is safer.