Yes; one which springs to mind in democratic Athens is the so-called 'mutilation of the herms' (stone phalluses, seemingly dedicated to Hermes although their 'function' is a matter of dispute, scattered throughout Athens) prior to the 'Sicilian Expedition' in the late 5th century BCE. This reportedly roused great dread and terror among the Athenians, and a perpetrator was sought.
Establishing solid facts is difficult owing to the nature of the evidence but according to Plutarch (who admittedly lived centuries after the fact), the mutilation of the herms was attributed to one Alcibiades by his enemy Androcles, using false witnesses as proof. Alcibiades was recalled from the expedition to Athens to stand trial, but he fled, resulting in a conviction in absentia, eventually defecting to Sparta.
Exactly who mutilated the herms, and why will likely never be known. But in my mind it certainly qualifies as terrorism, one way or the other.
Source (and further reading): Mark Henderson Munn (2000), 'The School of History: Athens in the Age of Socrates' pp 103-106
Terrorism is based on instilling fear in people, therefore it can't exist without modern mass media. Even if you massacred a group of people in the most gruesome manner in the middle ages, just a few people within a few km would learn about this immediately. Terrorism is an entirely modern phenomenon.