No, you cannot use the Integra harness in a '96+ Civic. The '92-'95 Civic's (EG's) and '94+ Integra's (DC's) use a 2 harness system. There is one harness on the engine and one that's in the car. In '96, they changed the Civics to one harness. It connects to the same plugs on the engine but instead of transfering to another harness before getting to the ECU, the harness goes straight through the firewall and connects directly to the ECU.

I'm assuming you didn't do your swap or are just planning one. Your going to have to use your existing Civic harness on the B17A and get an OBD II to OBD I conversion harness to use an OBD I ECU. An OBD II ECU will be looking for sensors and signals your OBD I engine simply doesn't have. Seeya.