Does the Old Testament say Satan incited David to take a census?

Both — and that's the point the two passages are making together.

If you read only 2 Samuel, it was YHWH who incited David:

"The anger of YHWH was kindled against Israel, and he incited David against them." — 2 Samuel 24:1

If you read only 1 Chronicles, it was Satan:

"And Satan stood against Israel and incited David to number Israel." — 1 Chronicles 21:1

The Hebrew verb in both verses is identical: vayyaset (וַיָּסֶת, H5496), "and he incited." Same verb form, same object (David), same action. One passage names YHWH; the other names the adversary. Both are true simultaneously. Chronicles isn't contradicting Samuel — it's naming the specific agent YHWH used to accomplish his judgment.

This pairing is one of the clearest illustrations of how the Old Testament holds divine sovereignty and adversarial agency together. The adversary is real and active, but he operates inside YHWH's governance, not independently of it. Job 2:3 makes this structure explicit: YHWH tells the adversary "you incited me against him" — using the same suth verb (H5496) to describe the adversary's instigation of God himself. The adversary's action becomes YHWH's action.

The word satan (שָׂטָן, H7854) itself traces a development across the Old Testament. In Numbers 22:22, YHWH's own holy angel plays the role of adversary to Balaam — the word there is just "an adversary," a role any agent can fill. In Job 1–2, all fourteen occurrences carry the definite article: ha-satan, "the Adversary" — a title for a specific figure in the divine court who plays the prosecutorial role. In 1 Chronicles 21:1, the latest Old Testament occurrence, the article is absent, which may signal a transition toward the personal name that becomes fully established when the New Testament opens with Satanas (Σατανᾶς, G4567).

Throughout that entire trajectory — common noun, definite title, personal name — the structural principle never changes: the adversary works within YHWH's explicit sovereignty.

For the full comparative table and the trajectory to Revelation 12:10, see the study The Silence and the Storm, section "The Development of the Adversary."