Ramban, in his commentary to this verse, says that it's the same rock mentioned earlier (Ex. 17:6):
...הִנְנִי עֹמֵד לְפָנֶיךָ שָּׁם עַל הַצּוּר בְּחֹרֵב
Behold, I will be standing before you there on the rock at Chorev...
He doesn't explain further. But perhaps we can say that in that case there seems to be a clear reason for the definite article; Moshe is being told to strike that particular rock in order to produce water for the people. So perhaps here Hashem is telling Moshe: "Last time I stood on this rock, and you were the one performing the action while I watched. This time the roles will be reversed: you will stand on the very same rock, and watch passively while I give a demonstration of My reality."
Conceivably, too, this is also related in another way to the next appearance of the word הַצּוּר in the Torah, in Deut. 32:4:
...הַצּוּר תָּמִים פָּעֱלוֹ, כִּי כָל דְּרָכָיו מִשְׁפָּט
The Rock, whose work is perfect, for all of His ways are just...
We are told (Talmud, Berachos 7a) that part of what Moshe was asking for ("Please show me Your ways") was to understand why sometimes the righteous suffer and the wicked have it good. He was informed that the true understanding of this is beyond human comprehension; at best we can see the answer in hindsight ("You shall see [only] My back"). In token of this, perhaps, Moshe declares at the end of his life, "Learn from my experience on *הַ*צּוּר, that rock! Hashem demonstrated to me there that the full understanding of how all of His doings are perfect and just is beyond even my abilities, but that it is no less true for all that."