A string group generated by involutions, or SGGI, is a pair $Γ=(G, S)$, where $G$ is a group and $S=\{ρ_0,\ldots, ρ_{r-1}\}$ is an ordered set of involutions generating $G$ and satisfying the commuting property: $$\forall i,j\in\{0,\ldots, r-1\}, \;|i-j|\ne 1\Rightarrow (ρ_iρ_j)^2=1.$$ When $S$ is an independent set, the rank of $Γ$ is the cardinality of $S$. We determine an upper bound for the rank of an SGGI over the alternating group of degree $n$. Our bound is tight when $n\equiv 0,1,4\pmod 5$.