  Quasicrystals represent a category of rarely structured solids that challenge
traditional periodicity in crystal materials. Recent advancements in the
synthesis of two-dimensional (2D) van der Waals materials have paved the way
for exploring the unique physical properties of these systems. Here, we report
on the synthesis of 2D quasicrystals featuring 30{\deg} alternating twist
angles between multiple graphene layers, using chemical vapor deposition (CVD).
Strikingly, we observed periodic Moir\'e patterns in the quasicrystal, a
finding that has not been previously reported in traditional alloy-based
quasicrystals. The Moir\'e periodicity, varying with the parity of the
constituent layers, aligns with the theoretical predictions that suggest a
stress cancellation mechanism in force. The emergence of Moir\'e fringes is
attributed to the spontaneous mismatched lattice constant in the oriented
graphene layers, proving the existence of atomic relaxation. This phenomenon,
which has been largely understudied in graphene systems with large twist
angles, has now been validated through our use of scanning transmission
electron microscopy (STEM). Our CVD-grown Moir\'e quasicrystal provides an
ideal platform for exploring the unusual physical properties that arise from
Moir\'e periodicity within quasicrystals.
