Male/female wire connectors - How to tell AWG/mm^2 rating?
A 20 AWG wire is rated for 5 A (see "American Wire Gauge"). Therefore you are looking for a connector with contact rating of 5 A sustained current or more.

You have many options. For a 2-pin (or 1-pin) connector you can pick an industrial-quality circular connector. It will be very safe and reliable, but it will cost you an arm and leg. Or you can pick a "one circuit" male pin and female receptacle with appropriate housing. BTW, if a connector has an "array" construction and more than one pin on a regular distance, this is called "pitch".

A good alternative to high-ampacity connectors has been developed in RC toy industry, primarily to connect batteries in toy boats/airplanes/cars/helicopters. They are coming in a naked form (various sizes of plugs/receptacles collectively referred as "banana" plugs), or have polarized and lockable housing. Here is an example from Banggood.com:



Surprisingly, it comes with full specifications (15 A DC rating etc.), and engineering-quality drawings. There are individual contacts of this sort, and smaller ones.