No. This rule isn't official at all. It is a homebrew variant.
Neither the PHB nor the DMG contain any mention of partial armor.
XGtE (which itself is official but optional) does not cover it either. This does not seem to be an optional rule, but rather a 3rd party/homebrew rule.
The partial armor homebrew rule on dandwiki (note the large "Homebrew Page" banner across the top) will make the equipment part of your game much more complicated. In 5e, you simply pay the price for or find a set of armor and wear it to get an AC which accounts for all of you armor (excepting Shields which can be added). Tracking a lot of armor is more suited to video games. It's much simpler to just track a suit of armor and add in any magic armor that you find (Helms, Gauntlets, Boots, etc.) which will provide magical bonuses but not AC bonuses (unless specifically detailed).
Also note that the rule shifts game balance quite a bit in favor of lightly armored martial types (including monks and barbarians!). It allows light armor users to achieve a much higher AC than allowed for under the rules without any penalty:
Normally a Ranger with +4 Dex would stick with Studded Leather for a 17 AC (12+5) rather than Half-Plate for 17 AC (15+2) since that incurs a Stealth penalty. Plate armor would grant 18 AC but requires a minimum strength and hurts your stealth.
With the partial armor rule, the Ranger could stick with Studded Leather and pile on a bunch or partial armor to easily exceed 20 AC (without a Shield), which is pretty unfair to the Paladin wearing Plate and a Shield.