  Inspired by a profound observation on the Racah--Wigner coefficients of
$U_q(\mathfrak{sl}_2)$, the Askey--Wilson algebras were introduced in the early
1990s. A universal analog $\triangle_q$ of the Askey--Wilson algebras was
recently studied. For $q$ not a root of unity, it is known that
$Z(\triangle_q)$ is isomorphic to the polynomial ring of four variables. A
presentation for $Z(\triangle_q)$ at $q$ a root of unity is displayed in this
paper. As an application, a presentation for the center of the double affine
Hecke algebra of type $(C_1^\vee,C_1)$ at roots of unity is obtained.
