Depends on the unique you're looking to copy.
UAs are practically impossible without a DLL mod. You could perhaps copy a few of the XML effects, but forget any modded Civilizations with Lua scripts.
UUs are by far the easiest Unique to copy, with the caveat that you aren't going to be able to just select them from the City production screen and build them normally. But there are all sorts of means in Lua to grant someone else's UU when certain conditions are met.
I've done it myself. Take a look at "Homura Akemi" in that pack.
UIs are doable, but you'd need a fair bit of Lua logic for it, you'd need to edit UnitPanel.lua extensively, and you'd need to figure out some way to help the AI utilize it. Not a project I'd recommend to a first-time modder.
UBs
were attempted, but it turned out to be infeasible, so much so that I helped them out with an upcoming rewrite of the UA to have different effects. The game makes way too many assumptions about what buildings you
should have for this to work well.