engine swap

I have a '89 civic si which is quite quick,but would it be possible to fit a b20a motor?

ya, you can fit any b-series engine into your car as long as you buy the mounts and everything else you will need to fit it right into the car

If you are talking about the b20 out of the late 80's earl 90's prelude then it won't work unless you make your own mounts. But even then it isn't worth it since there are so many other motors out there that will bolt in with a mount kit. If you are talking about the b20b/z from the crv then it will fit with minimal work.