Will a 90 Honda Prelude motor fit in an 89 Honda Civic DX?

No, the B20A or B21A motors will not fit into ANY other car than the 88-91 Prelude it was intended for. This is because the engine block was designed to sit at an 18-degree rearward slant in order to clear the low hood-line of the car. So these motors will not work in anything but a 3rd generation Prelude.

If you intend to make it work and swap a B20A or B21A motor into a 4th generation Honda Civic then by all means have fun, but it will be neither easy nor cheap to do so because a lot of custom fabrication will be involved. It would be a waste of time and money.