We study the Steklov problem on a subgraph with boundary (Ω,B) of a polynomial growth Cayley graph Γ. We prove that for each k ∈ℕ, the k^ eigenvalue tends to 0 proportionally to 1/|B|^1/d-1, where d represents the growth rate of Γ. The method consists in associating a manifold M to Γ and a bounded domain N ⊂ M to a subgraph (Ω, B) of Γ. We find upper bounds for the Steklov spectrum of N and transfer these bounds to (Ω, B) by discretizing N and using comparison Theorems.