  We introduce a notion of equivariant vector bundles on schemes over
semirings. We do this by considering the functor of points of a locally free
sheaf. We prove that every toric vector bundle on a toric scheme $X$ over an
idempotent semifield equivariantly splits as a sum of toric line bundles. We
then study the equivariant Picard group $\text{Pic}_G(X)$. Finally, we prove a
version of Klyachko's classification theorem for toric vector bundles over an
idempotent semifield.
