  A numerical semigroup $S$ is a cofinite, additively-closed subset of the
nonnegative integers that contains $0$. In this paper, we initiate the study of
atomic density, an asymptotic measure of the proportion of irreducible elements
in a given ring or semigroup, for semigroup algebras. It is known that the
atomic density of the polynomial ring $\mathbb{F}_q[x]$ is zero for any finite
field $\mathbb{F}_q$; we prove that the numerical semigroup algebra
$\mathbb{F}_q[S]$ also has atomic density zero for any numerical semigroup~$S$.
We also examine the particular algebra $\mathbb{F}_2[x^2,x^3]$ in more detail,
providing a bound on the rate of convergence of the atomic density as well as a
counting formula for irreducible polynomials using M\"{o}bius inversion,
comparable to the formula for irreducible polynomials over a finite field
$\mathbb{F}_q$.
