Tic refers to (1) a habitual spasmodic muscle movement, and (2) a recurrent trait or quirk. The word is only a noun.
Tick is both a noun and a verb. Its definitions include (1) a clicking sound, (2) a second or a moment, (3) a mark used to check off an item, and (4) a bloodsucking arachnid or louselike insect. Tick is also the correct spelling in the phrasal verb tick off, meaning (1) to anger, or (2) to check off (a list).
Examples
Tic
I have a nervous tic of scanning the foreign exchange rates for signs of trouble. [Telegraph]
She’s a scarily charismatic performer with exquisite control over every facial tic and limb-twist she brings to a character. [The Seattle Times]
Tick
Nonetheless, the team thinks the Heartland virus is also transmitted by ticks. [Los Angeles Times]
Yes, humidity will tick up a little bit by that point, but temperatures should only reach up into the 80s. [Washington Post]
Pop star Jay Kay has been ticked off by the National Trust after ruffling feathers by landing his helicopter in a bird sanctuary. [Mirror]
Thousands of people have left messages of support on Alice’s blog and many have even offered to help her tick off some of the items on her list. [CNN]