  Let $X$ be a smooth projective curve over the complex numbers. We compute the
Brauer group of the moduli stack of Bruhat-Tits group scheme
$\mathcal{G}$-torsors on $X$. When $g(X) \geq 3$ we compute the Brauer group of
the regularly stable locus of the coarse moduli space of semi-stable
$\mathcal{G}$-torsors.
