2000 Honda civic losing radiator fluid. There is no water in the oil, no visible leaks, no exhaust in the radiator, or water coming out the exhaust.

Could the radiator cap be the possible reason my 2000 civic loses radiator fluid?

You've definitely got a leak somewhere. If it was losing coolant at the cap, you'd see signs of it there. It's likely getting burned either in the engine (slowly and not yet affecting performance) or it's leaking onto the exhaust and burns off before leaving a stain.
A quality pressure test and a block test will tell you.

Wanted to add that the compression checked out ok.

Read your Owner's Manual on how to properly fill the cooling system. This will eliminate any entrapped air in the system. It's possible air in the system is being slowly purged and replaced by coolant, the level of which is dropping in the reservoir.