Rand's writing in Anthem has a uniquely primitive feel. It reads more like some ancient text than it does a mass-market paperback. In part, that's because of how simple and bare it is. There are very few details and the words are simple. The sentences are short and simply constructed. We often find Rand keeping individual sentences separate that could easily have been tied together, with the result that there's a certain repetitiveness and jerkiness to the writing:
We stopped when we felt hunger. We saw birds in the tree branches, and flying from under our footsteps. We picked a stone and we sent it as an arrow at a bird. It fell before us. We made a fire, we cooked the bird, and we ate it, and no meal had ever tasted better to us. And we thought suddenly that there was a great satisfaction to be found in the food which we need and obtain by our own hand. (8.5)
Rand also often uses language that sounds a little epic. It's full of grand but vague phrases like "the night of the ages" and invocations of great and timeless things like "the human heart" and "the race of men."
That sort of language has a unique power and forcefulness about it. In fact, all of those are elements of scriptural writing, of the sort you find in the Bible. The similarity is almost surely intentional, since part of what Rand is trying to do is claim for the human ego the language of the holy and the sacred.