No. If you have a 99 Civic EX, you use the 10.4" rotors. The Si has the same rotors, and 94-01 Integras (not R) have the same EXACT rotors. Upgrading requires new calipers for new rotors. The cheap way to do it, is get ITR calipers (92 Honda Accord Wagon uses the same caliper, just cheaper and easier to find). Then get 92-96 Prelude VTEC rotors redrilled to the 4x100 bolt pattern. This should go onto your stock knuckle. SOmeone verify this. If not, a Si knuckle or a 94-01 Integra LS knuckle will work.

One more note, you have to use 99-00 Si brake lines. and no, Integra ones wont work.