Every toric line bundle equipped with a toric section admits a unique structure of $\mathbb{T}$-equivariant line bundle such that the toric section becomes an invariant section. Conversely, every $\mathbb{T}$-equivariant toric line bundle admits a unique invariant toric section. Thus, there is a natural bijection between the space of $\mathbb{T}$-equivariant toric line bundles and the space of toric line bundles with a toric section. In particular, every line bundle admits a structure of $\mathbb{T}$-equivariant line bundle. This is not the case for higher rank vector bundles on toric varieties, nor for line bundles on other spaces with group actions like, for instance, elliptic curves.