Can you store cigars in a Ziploc bag?

Not for long periods of time. But if you're going to store them for a couple of days before you smoke them, you can place them in a Ziploc bag with a damp (not soaked) paper towel if your cigars are in cellophane wrappers. If they aren't, your cigars may get wet (which you definitely don't want).

If you are going to be smoking cigars in the future, it's a good idea to invest in a humidor.