Let $(M,\omega)$ be a compact symplectic manifold with $[\omega]$ integral. It is a Theorem of Gromov (1970) and Tischler (1977) that $(M,\omega)$ symplectically embeds into $\mathbb{C}P^n$ with the Fubini-Study symplectic form, for $n$ large enough. Let $\beta_1(M)$ be the first Betti number of $M$. We refine this result of Gromov and Tischler by showing that the weak homotopy type of the space of symplectic embeddings of such a symplectic manifold into $\mathbb{C}P^\infty$ is $(S^1)^{\beta_1(M)}\times\mathbb{C}P^\infty$.