Is it true that torsion subgroups of hyperbolic groups are finite?

I have a vague memory that this is true, perhaps due to Ol'shanskii, but have been struggling to find a reference.

(By a torsion subgroup I mean a subgroup $T\leq H$ such that every $t\in T$ has finite order. Although there are finitely many conjugacy classes of finite order elements in $H$, this does not immediately imply that $T$ is finite.)