To every rational complex curve C \subset (\mathbf{C}^\times)^n we associate a rational tropical curve \Gamma \subset \mathbf{R}^n so that the amoeba \mathcal{A}(C) \subset \mathbf{R}^n of C is within a bounded distance from \Gamma. In accordance with the terminology introduced by Passare and Rullgård, we call \Gamma the spine of \mathcal{A}(C). We use spines to describe tropical limits of sequences of rational complex curves.