The command given to a dog, “sic ’em,” derives from the word “seek.” The 1992 punk rock album titled Sick ’Em has helped popularize the common misspelling of this phrase. Unless you want to tell how you incited your pit bull to vomit on someone’s shoes, don’t write “sick ’em” or “sick the dog.”
The standard spelling of the “-ing” form of the word is “siccing.”
In a different context, the Latin word sic (“thus”) inserted into a quotation is an editorial comment calling attention to a misspelling or other error in the original which you do not want to be blamed for but are accurately reproducing: “She acted like a real pre-Madonna [sic].” When commenting on someone else’s faulty writing, you really want to avoid misspelling this word as sick.
Although it’s occasionally useful in preventing misunderstanding, sic is usually just a way of being snotty about someone else’s mistake, largely replaced now by “lol.” Sometimes it’s appropriate to correct the mistakes in writing you’re quoting; and when errors abound, you needn’t mark each one with a sic—your readers will notice.