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We prove an asymptotic formula as $x\to +\infty$ for the number of algebraicintegers $\alpha$ belonging to a fixed CM number field and satisfying$\alpha\overline{\alpha}\leq x$. This problem is related to the height zetafunction $Z_h(X^K,s)$ associated to the anticanonical class of a certain toricvariety $X^K$ over $\mathbb{Q}$ and we show that $Z_h(X^K,s)$ has a meromorphiccontinuation to the half-plane $\{\Re(s)>\frac{1}{2}\}$ where it is holomorphicexcept at $s=1$. Along the way we obtain a new proof of Manin's conjecture onthe asymptotic growth of points on $X^K(\mathbb{Q})$ of bounded height.

Croissance asymptotique de nombres de Weil appartenant \`a un corps de nombres fix\'e