You'll have a few issues you need to be aware of. The '93 tranny won't work, '92+ Hondas use a hydrolock system to engage the clutch, pre '91 Civic's use a cable. You can reuse the stock '90 civic's tranny in it's place though. You'll also have an issue if the '90 Civic isn't an Si. '88-'91 non-Si Civic's use a dual port injection where you have a TB and 2 injectors mounted together that work like a fuel injected carb as opposed to multiport injection that has 1 injector per cylinder mounted down by the head. You could either swap over the intake manifold/fuel system from the '90's old engine onto the new one and make the '93 engine dual port injection or convert the cars wiring harness and computer over to '88-'91 Si specs (multiport injection) wtih an Si's ECU to control it. The '90's ECU will only control 2 injectors and the '93 ECU won't plug into the '90 in-car harness (there are adaptors available to use the '93 ECU but will still require a multiport conversion and the addition of several wires like O2 sensor and what not).

Simpliest way to do it, take the '93 long block and strip everything off it and install all the old sensors and wiring harness from the '90 engine, including the intake manifold and the like. It will make a little less power than it would converted to MPFI but it will still work like the old engine used to and allow you to continue to use the '90 ECU (this is all assuming you don't have a '90 Si). If your in the mood to do some grunt and hunting work, converting the car to MPFI and running an Si ECU would be a fun project assuming it's not your only car.