Sort of.

Terrorism is a pretty broad concept. The FBI gives a nicely broad definition of "The unlawful use of force or violence against persons or property to intimidate or coerce a government, the civilian population, or any segment thereof in furtherance of political or social objectives." Since terrorism is a concept that has only existed since (disclaimer: not my field) the late 1700s in France and the mid to late 1800s in Russia before re-emerging as Islamic terrorism in the 1970's in Egypt, I should qualify that some of the historical examples I'm going to provide could probably be argued to have not been acts of terrorism but rather of war, or whatever.

The sicarii in Judea are the first group that comes to mind. They were a group of Jewish zealots that rebelled against Roman authority in Judea in the 60's AD, and their their method was to target Roman collaborators (not actual Romans, who were well guarded) with public stabbings, in order to intimidate Jewish collaborators. They contributed greatly to sparking a full-scale war with Rome, which is I'm sure what they wanted, but the result probably didn't please them so much: after multiple Jewish rebellions and unequivocal Roman victories, the Romans got tired of the whole business and conducted a total ethnic cleansing of the Jewish population of the middle east, the effects of which can be clearly seen today in the ruckus that dropping Israel in the middle of Palestine has caused.

Roman citizens were regularly targeted throughout the Republic and Empire by rebellious peoples. Mithridates VI of Pontus supposedly killed tens of thousands of Roman citizens in the East to show Rome he was sick of their crap, which ended badly for him and his empire. The Italians started the Social War with the killing of Roman citizens in the city of Picenum (could be wrong?), which ended with spectacular violence when Pompey Strabo took the place back. The revolt of Vercingetorix in 52 BC began with the mass slaughter of Roman citizens in Gaul, which was brutally avenged at Avaricum.

Aside from the sicarii, in the Early Empire/Principate perhaps the most spectacular example of something resembling terrorism was the sadistic mass killing of (allegedly) 80,000 Roman civilians (see Tacitus) by the Iceni in the rebellion of Boudicca, c. AD 60. Roman civilians east of the Rhine must have been targeted in the aftermath of the defeat of Varus in Germania in AD 9, and likewise with Romans in Illyria during the Great Revolt of AD 6-9.

But with what you're probably thinking with your question, targeted, public, symbolic, politically motivated killings of civilians such as those recently in France, aside from the obvious example of the sicarii (who didn't target actual Romans), terrorism probably wasn't a common thing under the Empire or Republic. While rebellions occurred and any rebellion would be bad for Roman civilians in the warzone, terrorism as we understand it now could not have been an effective tactic in the Roman Empire. The Romans did not value life as we do, and they did not value concepts we rattle off in opposition to terrorism like freedom or democracy. The Romans much preferred concepts like terror, courage and victory, and the authorities never did much care for the lives of civilians as long as it did not greatly effect the economy or more importantly, the military. If Islamic terrorists existed in the Roman Empire, which they didn't and could not have, the Romans would probably have responded with an ethnic cleansing such as the Jews experienced after their final rebellion was crushed c. AD 135, and they would have proceeded to continue their slow economic, cultural and military decline that caused the whole place to fall over in the 5th century AD.