Would a k20a R (RSX type R) engine fit in my 1990 honda civic with minimal mods to the engine bay and if so what esle would i need to do the engine swap. Thanks later  

Dont see why not.  The K20 and the B16 or B18 that are probably in your civic arent all that different in terms of size, the only thing i dont know is if the RSX-R has a LSD (which might affect mounting).

As for other parts, basically you'll need the wiring for both cars (all of it), the ECU (probably) and the transmissions (most likely).  Im no entirely sure what kind of work this would entail, but its certainly not for anyone.  

I think the K-series output shaft runs clockwise, while the D- and B-series went counter-clockwise (or vice versa, I don't remember), so that's a potential sticking point. HASport makes engine conversion kits for putting different Honda engines into Hondas they originally weren't designed to fit, they'll probably have a kit for stuffing a K-series into an EF-chassis Civic.

Another caveat: If you're talking about the JDM Integra (RSX) Type-R engine, you live in a state with emissions testing, and you plan on making the car street-legal, there may be emissions issues since that engine never made it to the US and was never smog-certified.  

it would fit but i'm not a fan of that swap, in those old civics i would go with a fully built non-vtec sohc carb motor, built right it makes those cars fun as hell.