It depends on if you're viewing terrorism as a concept (in other words, as a social construct where its meaning changes throughout time) or as an immutable act defined by certain essential characteristics (although what these characteristics are is widely debated). Social scientists tend to follow the latter conception, while those in the humanities follow the former.

If we are speaking of terrorism in the more essentialist understanding supported by social scientists, then terrorism is not new. It is defined by certain key characteristics although, as I said, these characteristics are heavily debated. The only characteristics that a majority of terrorism scholars support are: the use of violence or force (83.5%), political motivations (65%), and the emphasis on promoting fear or terror (51%). If we look only at these characteristics, we can easily push back the origins of terrorism basically to the beginning of civilization. Many scholars argue that terrorism has existed since the Assyrian Empire (c. 1300 BC), but more often to the Zealots of Palestine in the Roman Empire.

Historians, always attempting to contextualize, have largely opposed these essentialist narratives. They argue that terrorism is a much more recent phenomenon. Some believe that terrorism began with the French Revolution and the creation of the modern nation-state, because terrorism is to a large degree centered upon opposition to a state's institutional and social legitimacy. But even the French Revolution might be too soon. The sociologist Lisa Stampnitsky has shown that it wasn't until the 1960s that, within the academy and government, terrorism became seen as a unique form of political action. Before, terrorism was subsumed into other forms of more traditional political violence, particularly guerrilla warfare and insurgency. Joseba Zulaika has recently argued that it wasn't until the 1970s that the public began to see terrorism as a unique form of political action. To reach this conclusion, he looked at newspaper indices for the subject "terrorism" and its derivative etymological forms and found that the word was never used. The label terrorism today holds a great deal of ideological baggage, but newspapers until the 1970s defined what we today would call terrorism simply by the nature of the attack (bombing, assassination, kidnapping, etc.).

In other words, our contemporary understanding of terrorism as a concept is fairly new. I agree with Zulaika that it was probably around the 1960s that our modern understanding of the subject developed, although some historians like Beverly Gage argue that we can see it develop in the 1910s and 1920s. At the same time, as social scientists have pointed out, we can also see certain essential characteristics of terrorism throughout time, but to do so means to sometimes apply anachronistic labels onto acts of violence that would not be considered terrorism in the modern sense of the word. To be clear, this isn't inherently a bad thing. We can learn a great deal about terrorism by trying to glean its essential characteristics. We just need to be careful in doing so.

Edit: I forgot sources that I referenced.

Alex Schmid. Political Terrorism: A New Guide to Actors, Authors, Concepts, Data Bases, Theories, and Literature

Joseba Zulaika, Terrorism: The Self-Fulfilling Prophecy

Bevery Gage, The Day Wall Street Exploded: A Story of America in its First Age of Terror

Mikkel Thorup, An Intellectual History of Terror: War, Violence, and the State

Lisa Stampnitzky, Disciplining Terror: How Experts Invented "Terrorism".