Yes having a bad radiator cap can cause coolant loss without any other coolant leaks.
The radiator cap works to seal in the pressure in the cooling system of your vehicle and when the radiator cap doesn't seal in the pressure it causes the coolant in your system to boil.
The boiling of the coolant can cause some of the coolant to evaporate off so if you're losing coolant and you have no other leaks you should check your radiator cap and change it out.
You can also have a mechanic use a coolant pressure testing tool to check to see if there is a leak in the cooling system.
It's normal to lose a little bit of coolant over around 400 to 500 miles or so but you shouldn't lose that much coolant.
I would recommend changing the radiator cap every 2 to 5 years to keep your coolant system pressurized properly and to prevent overheating of the engine which can cause damage.