"Zecke" is an expression used by xenophobic right-wing extremists. It is named related to the "tick", a small little animal. It is extreme hostile. But I do not know exactly, whether the verb comes directly from this form.
"Anzecken" is slang and no part of the standard language. I agree with nerven oder anwidern - but I suppose, it has a rassistic or xenophobic connotation.
I never heard "anzecken" and it seems that it isn't used frequently. Google doesn't give a lot of entries.
A "Zecke" (tick) is an animal that lives on the blood of other beings by sucking their blood. The verb "anzecken" could mean the action a tick does by biting the person or animal in order to get their blood. It's a parasite.