Retrieval-Augmented Generation (RAG) injects LLM queries with relevant documents to improve response quality. This injection increases prompt length and slows time to first token (TTFT). Unlike standard queries, RAG queries have a unique property of context reuse where the same documents recur across user queries. Thus, fully recomputing documents for every RAG query does redundant compute and increases TTFT. Prior works precompute KV tensors of RAG documents offline and coarsely recompute some tokens during online prefill. However, such KV reuse is often slower than full recomputation on modern GPUs due to high-latency disk transfers. Further, such a coarse-grained recomputation degrades accuracy. To address these limitations, this paper proposes SIFT: Selective-Index For Fast Compute of RAG Prefill by Exploiting Attention Invariance. SIFT processes documents offline and extracts fine-grained locations of high attention scores for each document. Next, we identify the following attention invariance insights that enable us to exploit the extracted locations during runtime: (1) Local-Attention Invariance: The location of high attention scores within a document remain invariant to surrounding documents. This helps us predict the location of high scores where the document attends to itself. (2) Cross-Attention Consistency: Keys with high intra-document attention also attract cross-attention from subsequent documents. This helps us predict the location of high scores where the document attends to future documents. Critically, SIFT stores no KV data and only stores locations of high scores in the form of two compact bit vectors. SIFT's storage is up to 24,000x smaller than KV tensors, obviating costly disk transfers. During prefill, SIFT computes the attention only for the marked locations and improves TTFT by 1.71x while holding accuracy within 1% of full recompute.