The verb sic, as to sic a dog on someone, is spelled “sic,” though “sick” is also accepted.
The various conjugations can use either a double-c or a ck, e.g., “He sicced the dogs on the intruder” or “I’ll be sicking this Rottweiler on you if you don’t clear out now.”
While either the c or ck is used, the former is considered “better” in many circles, the latter a “well, a lot of people do it this way, too, so we have to mention it” variant. That may or may not be true (the OED seems to prefer sick as the older form).
It is a dialectical variation on seek.